1000 (number)

(Redirected from 1789 (number))

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

← 999 1000 1001 →
Cardinalone thousand
Ordinal1000th
(one thousandth)
Factorization23 × 53
Divisors1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
Greek numeral,Α´
Roman numeralM
Roman numeral (unicode)M, m, ↀ
Unicode symbol(s)
Greek prefixchilia
Latin prefixmilli
Binary11111010002
Ternary11010013
Senary43446
Octal17508
Duodecimal6B412
Hexadecimal3E816
Tamil
Chinese
Punjabi੧੦੦੦
Devanagari१०००

A group of one thousand things is sometimes known, from Ancient Greek, as a chiliad.[1] A period of one thousand years may be known as a chiliad or, more often from Latin, as a millennium. The number 1000 is also sometimes described as a short thousand in medieval contexts where it is necessary to distinguish the Germanic concept of 1200 as a long thousand.

Notation edit

  • The decimal representation for one thousand is
  • The SI prefix for a thousand units is "kilo-", abbreviated to "k"—for instance, a kilogram or "kg" is a thousand grams. This is sometimes extended to non-SI contexts, such as "ka" (kiloannum) being used as a shorthand for periods of 1000 years. In computer science, however, "kilo-" is used more loosely to mean 2 to the 10th power (1024).
  • In the SI writing style, a non-breaking space can be used as a thousands separator, i.e., to separate the digits of a number at every power of 1000.
  • Multiples of thousands are occasionally represented by replacing their last three zeros with the letter "K" or "k": for instance, writing "$30k" for $30 000 or denoting the Y2K computer bug of the year 2000.
  • A thousand units of currency, especially dollars or pounds, are colloquially called a grand. In the United States, this is sometimes abbreviated with a "G" suffix.

Properties edit

1000 is the 10th icositetragonal number, or 24-gonal number.[2] It is also the 16th generalized 30-gonal number.[3]

1000 is the Wiener index of cycle length 20, also the sum of labeled boxes arranged as a pyramid with base 1 – 20.[4][5][6][a]

1000 is the element of multiplicity in a   toroidal board in the n-Queens problem,[8] with respective indicator of 25[9] and count of 51.[10][11]

1000 is the number of strict partitions of 50 containing the sum of no subset of the parts.[12]

 
The regular polygram {1000/499} of the chiliagon, where its diagonals do not pass through the center, yet are closest to it (indistinguishably, unless one zooms in).

A chiliagon is a 1000-sided polygon,[13][14] of order 2000 in its regular form.[b]

Totient values edit

1000 has a reduced totient value   of 100,[20] and Euler totient   of 400.[16]

11 integers have a totient value of 1000 (1111, 1255, ..., 3750).[16]

One thousand is also equal to the sum of Euler's totient summatory function   over the first 57 integers.[21]

Repdigits edit

In decimal, multiples of one thousand are totient values of four-digit repdigits:[16]

Notice, that in the list of composite numbers, 7777 is very nearly the composite index of 8888: 8886 is the 7779th composite number.[22] Also,[16]

  • 5000 has a totient value of 2000, as does 5050 = 2025 + 3025 = 452 + 552, where
  • 3000, 5000 and 7000 are the three multiples of one thousand, less than 104, to not be totient values of four-digit repdigits;
  • 10000 has a totient value of 4000. The totient of 1000 is 400, of 100 it is 40, and of 10 it is 4.

1600 = 402 is the totient value of 4000, as well as 6000, whose collective sum is 10000, where 6000 is the totient of 9999, one less than 104.[16][c]

The sum of the first nine prime numbers up to 23 is 100, with  , where   is the number of integer partitions of 23.[28]

Prime values edit

Using decimal representation as well,

  • 997 is the 168th and largest prime number less than 1000,[25] while
  • 97 is the 25th and largest prime number less than 100; with
  • 9 and 7 respectively the (4th) largest composite and prime less than 10.[22][25]

On the other hand, the largest prime number less than 10000 is the 1229th prime number, 9973.[25][d]

1000 is also the smallest number in base-ten that generates three primes in the fastest way possible by concatenation with decremented numbers:[37]

  • 1,000,999
  • 1,000,999,998,997
  • 1,000,999,998,997,996,995,994,993

all represent prime numbers.[38][39]

The one-thousandth prime number is 7919. It is a difference of 1 from the order of the smallest sporadic group:  .[40][41]

Numbers in the range 1001–1999 edit

1001 to 1099 edit

1001 = sphenic number (7 × 11 × 13), pentagonal number, pentatope number, palindromic number
1002 = sphenic number, Mertens function zero, abundant number, number of partitions of 22
1003 = the product of some prime p and the pth prime, namely p = 17.
1004 = heptanacci number[42]
1005 = Mertens function zero, decagonal pyramidal number[43]
1006 = semiprime, product of two distinct isolated primes (2 and 503); unusual number; square-free number; number of compositions (ordered partitions) of 22 into squares; sum of two distinct pentatope numbers (5 and 1001); number of undirected Hamiltonian paths in 4 by 5 square grid graph;[44] record gap between twin primes;[45] number that is the sum of 7 positive 5th powers.[46] In decimal: equidigital number; when turned around, the number looks like a prime, 9001; its cube can be concatenated from other cubes, 1_0_1_8_1_0_8_216 ("_" indicates concatenation, 0 = 03, 1 = 13, 8 = 23, 216 = 63)[47]
1007 = number that is the sum of 8 positive 5th powers[48]
1008 = divisible by the number of primes below it
1009 = smallest four-digit prime, palindromic in bases 11, 15, 19, 24 and 28: (83811, 47415, 2F219, 1I124, 18128). It is also a Lucky prime and Chen prime.
1010 = 103 + 10,[49] Mertens function zero
1011 = the largest n such that 2n contains 101 and does not contain 11011, Harshad number in bases 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75 (and 202 other bases), number of partitions of 1 into reciprocals of positive integers <= 16 Egyptian fraction[50]
1012 = ternary number, (3210) quadruple triangular number (triangular number is 253),[51] number of partitions of 1 into reciprocals of positive integers <= 17 Egyptian fraction[50]
1013 = Sophie Germain prime,[52] centered square number,[53] Mertens function zero
1014 = 210-10,[54] Mertens function zero, sum of the nontriangular numbers between successive triangular numbers
1015 = square pyramidal number[55]
1016 = member of the Mian–Chowla sequence,[56] stella octangula number, number of surface points on a cube with edge-length 14[57]
1017 = generalized triacontagonal number[58]
1018 = Mertens function zero, 101816 + 1 is prime[59]
1019 = Sophie Germain prime,[52] safe prime,[60] Chen prime
1020 = polydivisible number
1021 = twin prime with 1019. It is also a Lucky prime.
1022 = Friedman number
1023 = sum of five consecutive primes (193 + 197 + 199 + 211 + 223);[61] the number of three-dimensional polycubes with 7 cells;[62] number of elements in a 9-simplex; highest number one can count to on one's fingers using binary; magic number used in Global Positioning System signals.
1024 = 322 = 45 = 210, the number of bytes in a kilobyte (in 1999, the IEC coined kibibyte to use for 1024 with kilobyte being 1000, but this convention has not been widely adopted). 1024 is the smallest 4-digit square and also a Friedman number.
1025 = Proth number 210 + 1; member of Moser–de Bruijn sequence, because its base-4 representation (1000014) contains only digits 0 and 1, or it's a sum of distinct powers of 4 (45 + 40); Jacobsthal-Lucas number; hypotenuse of primitive Pythagorean triangle
1026 = sum of two distinct powers of 2 (1024 + 2)
1027 = sum of the squares of the first eight primes; can be written from base 2 to base 18 using only the digits 0 to 9.
1028 = sum of totient function for first 58 integers; can be written from base 2 to base 18 using only the digits 0 to 9; number of primes <= 213.[63]
1029 = can be written from base 2 to base 18 using only the digits 0 to 9.
1030 = generalized heptagonal number
1031 = exponent and number of ones for the fifth base-10 repunit prime,[64] Sophie Germain prime,[52] super-prime, Chen prime
1032 = sum of two distinct powers of 2 (1024 + 8)
1033 = emirp, twin prime with 1031
1034 = sum of 12 positive 9th powers[65]
1035 = triangular number,[66] hexagonal number[67]
1036 = central polygonal number[68]
1037 = number in E-toothpick sequence[69]
1038 = even integer that is an unordered sum of two primes in exactly n ways[70]
1039 = prime of the form 8n+7,[71] number of partitions of 30 that do not contain 1 as a part,[72] Chen prime
1040 = 45 + 42: sum of distinct powers of 4.[73] The number of pieces that could be seen in a 6 × 6 × 6× 6 Rubik's Tesseract.
1041 = sum of 11 positive 5th powers[74]
1042 = sum of 12 positive 5th powers[75]
1043 = number whose sum of even digits and sum of odd digits are even[76]
1044 = sum of distinct powers of 4[73]
1045 = octagonal number[77]
1046 = coefficient of f(q) (3rd order mock theta function)[78]
1047 = number of ways to split a strict composition of n into contiguous subsequences that have the same sum[79]
1048 = number of partitions of n into squarefree parts[80]
1049 = Sophie Germain prime,[52] highly cototient number,[81] Chen prime
1050 = 10508 to decimal becomes a pronic number (55210),[82] number of parts in all partitions of 29 into distinct parts[83]
1051 = centered pentagonal number,[84] centered decagonal number
1052 = number that is the sum of 9 positive 6th powers[85]
1053 = triangular matchstick number[86]
1054 = centered triangular number[87]
1055 = number that is the sum of 12 positive 6th powers[88]
1056 = pronic number[89]
1057 = central polygonal number[90]
1058 = number that is the sum of 4 positive 5th powers,[91] area of a square with diagonal 46[92]
1059 = number n such that n4 is written in the form of a sum of four positive 4th powers[93]
1060 = sum of the first 25 primes from 2 through 97 (the number of primes less than 100),[94] and sixth sum of 10 consecutive primes, starting with 23 through 131.[95]
1061 = emirp, twin prime with 1063, number of prime numbers having four digits[96]
1062 = number that is not the sum of two palindromes[97]
1063 = super-prime, sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167); near-wall-sun-sun prime[98]
1064 = sum of two positive cubes[99]
1065 = generalized duodecagonal[100]
1066 = number whose sum of their divisors is a square[101]
1067 = number of strict integer partitions of n in which are empty or have smallest part not dividing the other ones[102]
1068 = number that is the sum of 7 positive 5th powers,[46] total number of parts in all partitions of 15[103]
1069 = emirp[104]
1070 = number that is the sum of 9 positive 5th powers[105]
1071 = heptagonal number[106]
1072 = centered heptagonal number[107]
1073 = number that is the sum of 12 positive 5th powers[75]
1074 = number that is not the sum of two palindromes[97]
1075 = number non-sum of two palindromes[97]
1076 = number of strict trees weight n[108]
1077 = number where 7 outnumbers every other digit in the number[109]
1078 = Euler transform of negative integers[110]
1079 = every positive integer is the sum of at most 1079 tenth powers.
1080 = pentagonal number[111]
1081 = triangular number,[66] member of Padovan sequence[112]
1082 = central polygonal number[68]
1083 = three-quarter square,[113] number of partitions of 53 into prime parts
1084 = third spoke of a hexagonal spiral,[114] 108464 + 1 is prime
1085 = number of partitions of n into distinct parts > or = 2[115]
1086 = Smith number,[116] sum of totient function for first 59 integers
1087 = super-prime, cousin prime, lucky prime[117]
1088 = octo-triangular number, (triangular number result being 136)[118] sum of two distinct powers of 2, (1024 + 64)[119] number that is divisible by exactly seven primes with the inclusion of multiplicity[120]
1089 = 332, nonagonal number, centered octagonal number, first natural number whose digits in its decimal representation get reversed when multiplied by 9.[121]
1090 = sum of 5 positive 5th powers[122]
1091 = cousin prime and twin prime with 1093
1092 = divisible by the number of primes below it
1093 = the smallest Wieferich prime (the only other known Wieferich prime is 3511[123]), twin prime with 1091 and star number[124]
1094 = sum of 9 positive 5th powers,[105] 109464 + 1 is prime
1095 = sum of 10 positive 5th powers,[125] number that is not the sum of two palindromes
1096 = hendecagonal number,[126] number of strict solid partitions of 18[127]
1097 = emirp,[104] Chen prime
1098 = multiple of 9 containing digit 9 in its base-10 representation[128]
1099 = number where 9 outnumbers every other digit[129]

1100 to 1199 edit

1100 = number of partitions of 61 into distinct squarefree parts[130]
1101 = pinwheel number[131]
1102 = sum of totient function for first 60 integers
1103 = Sophie Germain prime,[52] balanced prime[132]
1104 = Keith number[133]
1105 = 332 + 42 = 322 + 92 = 312 + 122 = 232 + 242, Carmichael number,[134] magic constant of n × n normal magic square and n-queens problem for n = 13, decagonal number,[135] centered square number,[53] Fermat pseudoprime[136]
1106 = number of regions into which the plane is divided when drawing 24 ellipses[137]
1107 = number of non-isomorphic strict T0 multiset partitions of weight 8[138]
1108 = number k such that k64 + 1 is prime
1109 = Friedlander-Iwaniec prime,[139] Chen prime
1110 = k such that 2k + 3 is prime[140]
1111 = 11 × 101, palindrome that is a product of two palindromic primes[141]
1112 = k such that 9k - 2 is a prime[142]
1113 = number of strict partions of 40[143]
1114 = number of ways to write 22 as an orderless product of orderless sums[144]
1115 = number of partitions of 27 into a prime number of parts[145]
1116 = divisible by the number of primes below it
1117 = number of diagonally symmetric polyominoes with 16 cells,[146] Chen prime
1118 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,21}[147]
1119 = number of bipartite graphs with 9 nodes[148]
1120 = number k such that k64 + 1 is prime
1121 = number of squares between 342 and 344.[149]
1122 = pronic number,[89] divisible by the number of primes below it
1123 = balanced prime[132]
1124 = Leyland number[150] = 210 + 102, spy number
1125 = Achilles number
1126 = number of 2 × 2 non-singular integer matrices with entries from {0, 1, 2, 3, 4, 5}[151]
1127 = maximal number of pieces that can be obtained by cutting an annulus with 46 cuts[152]
1128 = triangular number,[66] hexagonal number,[67] divisible by the number of primes below it
1129 = number of lattice points inside a circle of radius 19[153]
1130 = skiponacci number[154]
1131 = number of edges in the hexagonal triangle T(26)[155]
1132 = number of simple unlabeled graphs with 9 nodes of 2 colors whose components are complete graphs[156]
1133 = number of primitive subsequences of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}[157]
1134 = divisible by the number of primes below it, triangular matchstick number[86]
1135 = centered triangular number[158]
1136 = number of independent vertex sets and vertex covers in the 7-sunlet graph[159]
1137 = sum of values of vertices at level 5 of the hyperbolic Pascal pyramid[160]
1138 = recurring number in the works of George Lucas and his companies, beginning with his first feature film – THX 1138; particularly, a special code for Easter eggs on Star Wars DVDs.
1139 = wiener index of the windmill graph D(3,17)[161]
1140 = tetrahedral number[162]
1141 = 7-Knödel number[163]
1142 = n such that n32 + 1 is prime,[164] spy number
1143 = number of set partitions of 8 elements with 2 connectors[165]
1144 is not the sum of a pair of twin primes[166]
1145 = 5-Knödel number[167]
1146 is not the sum of a pair of twin primes[166]
1147 = 31 × 37 (a product of 2 successive primes)[168]
1148 is not the sum of a pair of twin primes[166]
1149 = a product of two palindromic primes[169]
1150 = number of 11-iamonds without bilateral symmetry.[170]
1151 = first prime following a prime gap of 22,[171] Chen prime
1152 = highly totient number,[172] 3-smooth number (27×32), area of a square with diagonal 48,[92] Achilles number
1153 = super-prime, Proth prime[173]
1154 = 2 × 242 + 2 = number of points on surface of tetrahedron with edgelength 24[174]
1155 = number of edges in the join of two cycle graphs, both of order 33[175]
1156 = 342, octahedral number,[176] centered pentagonal number,[84] centered hendecagonal number.[177]
1157 = smallest number that can be written as n^2+1 without any prime factors that can be written as a^2+1.[178]
1158 = number of points on surface of octahedron with edgelength 17[179]
1159 = member of the Mian–Chowla sequence,[56] a centered octahedral number[180]
1160 = octagonal number[181]
1161 = sum of the first 26 primes
1162 = pentagonal number,[111] sum of totient function for first 61 integers
1163 = smallest prime > 342.[182] See Legendre's conjecture. Chen prime.
1164 = number of chains of multisets that partition a normal multiset of weight 8, where a multiset is normal if it spans an initial interval of positive integers[183]
1165 = 5-Knödel number[167]
1166 = heptagonal pyramidal number[184]
1167 = number of rational numbers which can be constructed from the set of integers between 1 and 43[185]
1168 = antisigma(49)[186]
1169 = highly cototient number[81]
1170 = highest possible score in a National Academic Quiz Tournaments (NAQT) match
1171 = super-prime
1172 = number of subsets of first 14 integers that have a sum divisible by 14[187]
1173 = number of simple triangulation on a plane with 9 nodes[188]
1174 = number of widely totally strongly normal compositions of 16
1175 = maximal number of pieces that can be obtained by cutting an annulus with 47 cuts[152]
1176 = triangular number[66]
1177 = heptagonal number[106]
1178 = number of surface points on a cube with edge-length 15[57]
1179 = number of different permanents of binary 7*7 matrices[189]
1180 = smallest number of non-integral partitions into non-integral power >1000.[190]
1181 = smallest k over 1000 such that 8*10^k-49 is prime.[191]
1182 = number of necklaces possible with 14 beads of 2 colors (that cannot be turned over)[192]
1183 = pentagonal pyramidal number
1184 = amicable number with 1210[193]
1185 = number of partitions of 45 into pairwise relatively prime parts[194]
1186 = number of diagonally symmetric polyominoes with 15 cells,[146] number of partitions of 54 into prime parts
1187 = safe prime,[60] Stern prime,[195] balanced prime,[132] Chen prime
1188 = first 4 digit multiple of 18 to contain 18[196]
1189 = number of squares between 352 and 354.[149]
1190 = pronic number,[89] number of cards to build an 28-tier house of cards[197]
1191 = 352 - 35 + 1 = H35 (the 35th Hogben number)[198]
1192 = sum of totient function for first 62 integers
1193 = a number such that 41193 - 31193 is prime, Chen prime
1194 =number of permutations that can be reached with 8 moves of 2 bishops and 1 rook on a 3 × 3 chessboard[199]
1195 = smallest four digit number for which a−1(n) is an integer is a(n) is 2*a(n-1) - (-1)n[200]
1196 =  [201]
1197 = pinwheel number[131]
1198 = centered heptagonal number[107]
1199 = area of the 20th conjoined trapezoid[202]

1200 to 1299 edit

1200 = the long thousand, ten "long hundreds" of 120 each, the traditional reckoning of large numbers in Germanic languages, the number of households the Nielsen ratings sample,[203] number k such that k64 + 1 is prime
1201 = centered square number,[53] super-prime, centered decagonal number
1202 = number of regions the plane is divided into by 25 ellipses[137]
1203: first 4 digit number in the coordinating sequence for the (2,6,∞) tiling of the hyperbolic plane[204]
1204: magic constant of a 7 × 7 × 7 magic cube[205]
1205 = number of partitions of 28 such that the number of odd parts is a part[206]
1206 = 29-gonal number [207]
1207 = composite de Polignac number[208]
1208 = number of strict chains of divisors starting with the superprimorial A006939(3)[209]
1209 = The product of all ordered non-empty subsets of {3,1} if {a,b} is a||b: 1209=1*3*13*31
1210 = amicable number with 1184[210]
1211 = composite de Polignac number[208]
1212 =  , where   is the number of partions of  [211]
1213 = emirp
1214 = sum of first 39 composite numbers,[212] spy number
1215 = number of edges in the hexagonal triangle T(27)[155]
1216 = nonagonal number[213]
1217 = super-prime, Proth prime[173]
1218 = triangular matchstick number[86]
1219 = Mertens function zero, centered triangular number[158]
1220 = Mertens function zero, number of binary vectors of length 16 containing no singletons[214]
1221 = product of the first two digit, and three digit repdigit
1222 = hexagonal pyramidal number
1223 = Sophie Germain prime,[52] balanced prime, 200th prime number[132]
1224 = number of edges in the join of two cycle graphs, both of order 34[175]
1225 = 352, square triangular number,[215] hexagonal number,[67] centered octagonal number,[216] icosienneagonal,[217] hexacontagonal[218] and hecatonicositetragonal (124-gonal).
1226 = number of rooted identity trees with 15 nodes [219]
1227 = smallest number representable as the sum of 3 triangular numbers in 27 ways[220]
1228 = sum of totient function for first 63 integers
1229 = Sophie Germain prime,[52] number of primes between 0 and 10000, emirp
1230 = the Mahonian number: T(9, 6)[221]
1231 = smallest mountain emirp, as 121, smallest mountain number is 11 × 11
1232 = number of labeled ordered set of partitions of a 7-set into odd parts[222]
1233 = 122 + 332
1234 = number of parts in all partitions of 30 into distinct parts,[83] smallest whole number containing all numbers from 1 to 4
1235 = excluding duplicates, contains the first four Fibbonacci numbers [223]
1236 = 617 + 619: sum of twin prime pair[224]
1237 = prime of the form 2p-1
1238 = number of partitions of 31 that do not contain 1 as a part[72]
1239 = toothpick number in 3D[225]
1240 = square pyramidal number[55]
1241 = centered cube number,[226] spy number
1242 = decagonal number[135]
1243 = composite de Polignac number[208]
1244 = number of complete partitions of 25[227]
1245 = Number of labeled spanning intersecting set-systems on 5 vertices.[228]
1246 = number of partitions of 38 such that no part occurs more than once[229]
1247 = pentagonal number[111]
1248 = the first four powers of 2 concatenated together
1249 = emirp, trimorphic number[230]
1250 = area of a square with diagonal 50[92]
1251 = 2 × 252 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 25[231]
1252 = 2 × 252 + 2 = number of points on surface of tetrahedron with edgelength 25[174]
1253 = number of partitions of 23 with at least one distinct part[232]
1254 = number of partitions of 23 into relatively prime parts[233]
1255 = Mertens function zero, number of ways to write 23 as an orderless product of orderless sums,[144] number of partitions of 23[234]
1256 = 1 × 2 × (52)2 + 6,[235] Mertens function zero
1257 = number of lattice points inside a circle of radius 20[153]
1258 = 1 × 2 × (52)2 + 8,[235] Mertens function zero
1259 = highly cototient number[81]
1260 = highly composite number,[236] pronic number,[89] the smallest vampire number,[237] sum of totient function for first 64 integers, number of strict partions of 41[143] and appears twice in the Book of Revelation
1261 = star number,[124] Mertens function zero
1262 = maximal number of regions the plane is divided into by drawing 36 circles[238]
1263 = rounded total surface area of a regular tetrahedron with edge length 27[239]
1264 = sum of the first 27 primes
1265 = number of rooted trees with 43 vertices in which vertices at the same level have the same degree[240]
1266 = centered pentagonal number,[84] Mertens function zero
1267 = 7-Knödel number[163]
1268 = number of partitions of 37 into prime power parts[241]
1269 = least number of triangles of the Spiral of Theodorus to complete 11 revolutions[242]
1270 = 25 + 24×26 + 23×27,[243] Mertens function zero
1271 = sum of first 40 composite numbers[212]
1272 = sum of first 41 nonprimes[244]
1273 = 19 × 67 = 19 × prime(19)[245]
1274 = sum of the nontriangular numbers between successive triangular numbers
1275 = triangular number,[66] sum of the first 50 natural numbers
1276 = number of irredundant sets in the 25-cocktail party graph[246]
1277 = the start of a prime constellation of length 9 (a "prime nonuple")
1278 = number of Narayana's cows and calves after 20 years[247]
1279 = Mertens function zero, Mersenne prime exponent
1280 = Mertens function zero, number of parts in all compositions of 9[248]
1281 = octagonal number[181]
1282 = Mertens function zero, number of partitions of 46 into pairwise relatively prime parts[194]
1283 = safe prime[60]
1284 = 641 + 643: sum of twin prime pair[224]
1285 = Mertens function zero, number of free nonominoes, number of parallelogram polyominoes with 10 cells.[249]
1286 = number of inequivalent connected planar figures that can be formed from five 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree[250]
1287 =  [251]
1288 = heptagonal number[106]
1289 = Sophie Germain prime,[52] Mertens function zero
1290 =  , average of a twin prime pair[252]
1291 = largest prime < 64,[253] Mertens function zero
1292 = number such that phi(1292) = phi(sigma(1292)),[254] Mertens function zero
1293 =  [255]
1294 = rounded volume of a regular octahedron with edge length 14[256]
1295 = number of edges in the join of two cycle graphs, both of order 35[175]
1296 = 362 = 64, sum of the cubes of the first eight positive integers, the number of rectangles on a normal 8 × 8 chessboard, also the maximum font size allowed in Adobe InDesign
1297 = super-prime, Mertens function zero, pinwheel number[131]
1298 = number of partitions of 55 into prime parts
1299 = Mertens function zero, number of partitions of 52 such that the smallest part is greater than or equal to number of parts[257]

1300 to 1399 edit

1300 = Sum of the first 4 fifth powers, mertens function zero, largest possible win margin in an NAQT match; smallest even odd-factor hyperperfect number
1301 = centered square number,[53] Honaker prime,[258] number of trees with 13 unlabeled nodes[259]
1302 = Mertens function zero, number of edges in the hexagonal triangle T(28)[155]
1303 = prime of form 21n+1 and 31n+1[260][261]
1304 = sum of 13046 and 1304 9 which is 328+976
1305 = triangular matchstick number[86]
1306 = Mertens function zero. In base 10, raising the digits of 1306 to powers of successive integers equals itself: 1306 = 11 + 32 + 03 + 64. 135, 175, 518, and 598 also have this property. Centered triangular number.[158]
1307 = safe prime[60]
1308 = sum of totient function for first 65 integers
1309 = the first sphenic number followed by two consecutive such number
1310 = smallest number in the middle of a set of three sphenic numbers
1311 = number of integer partitions of 32 with no part dividing all the others[262]
1312 = member of the Mian-Chowla sequence;[56]
1313 = sum of all parts of all partitions of 14 [263]
1314 = number of integer partitions of 41 whose distinct parts are connected[264]
1315 = 10^(2n+1)-7*10^n-1 is prime.[265]
1316 = Euler transformation of sigma(11)[266]
1317 = 1317 Only odd four digit number to divide the concatenation of all number up to itself in base 25[267]
1318512 + 1 is prime,[268] Mertens function zero
1319 = safe prime[60]
1320 = 659 + 661: sum of twin prime pair[224]
1321 = Friedlander-Iwaniec prime[139]
1322 = area of the 21st conjoined trapezoid[202]
1323 = Achilles number
1324 = if D(n) is the nth representation of 1, 2 arranged lexicographically. 1324 is the first non-1 number which is D(D(x))[269]
1325 = Markov number,[270] centered tetrahedral number[271]
1326 = triangular number,[66] hexagonal number,[67] Mertens function zero
1327 = first prime followed by 33 consecutive composite numbers
1328 = sum of totient function for first 66 integers
1329 = Mertens function zero, sum of first 41 composite numbers[212]
1330 = tetrahedral number,[150] forms a Ruth–Aaron pair with 1331 under second definition
1331 = 113, centered heptagonal number,[107] forms a Ruth–Aaron pair with 1330 under second definition. This is the only non-trivial cube of the form x2 + x − 1, for x = 36.
1332 = pronic number[89]
1333 = 372 - 37 + 1 = H37 (the 37th Hogben number)[198]
1334 = maximal number of regions the plane is divided into by drawing 37 circles[238]
1335 = pentagonal number,[111] Mertens function zero
1336 = sum of gcd(x, y) for 1 <= x, y <= 24,[272] Mertens function zero
1337 = Used in the novel form of spelling called leet. Approximate melting point of gold in kelvins.
1338 = atomic number of the noble element of period 18,[273] Mertens function zero
1339 = First 4 digit number to appear twice in the sequence of sum of cubes of primes dividing n[274]
1340 = k such that 5 × 2k - 1 is prime[275]
1341 = First mountain number with 2 jumps of more than one.
1342 =  ,[201] Mertens function zero
1343 = cropped hexagone[276]
1344 = 372 - 52, the only way to express 1344 as a difference of prime squares[277]
1345 = k such that k, k+1 and k+2 are products of two primes[278]
1346= number of locally disjointed rooted trees with 10 nodes[279]
1347 = concatenation of first 4 Lucas numbers [280]
1348 = number of ways to stack 22 pennies such that every penny is in a stack of one or two[281]
1349 = Stern-Jacobsthal number[282]
1350 = nonagonal number[213]
1351 = number of partitions of 28 into a prime number of parts[145]
1352 = number of surface points on a cube with edge-length 16,[57] Achilles number
1353 = 2 × 262 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 26[231]
1354 = 2 × 262 + 2 = number of points on surface of tetrahedron with edgelength 26[174]
1355 appears for the first time in the Recamán's sequence at n = 325,374,625,245.[283] Or in other words A057167(1355) = 325,374,625,245[284][285]
1356 is not the sum of a pair of twin primes[166]
1357 = number of nonnegative solutions to x2 + y2 ≤ 412[286]
1358 = rounded total surface area of a regular tetrahedron with edge length 28[239]
1359 is the 42d term of Flavius Josephus's sieve[287]
1360 = 372 - 32, the only way to express 1360 as a difference of prime squares[277]
1361 = first prime following a prime gap of 34,[171] centered decagonal number, Honaker prime[258]
1362 = number of achiral integer partitions of 48[288]
1363 = the number of ways to modify a circular arrangement of 14 objects by swapping one or more adjacent pairs[289]
1364 = Lucas number[290]
1365 = pentatope number[291]
1366 = Arima number, after Yoriyuki Arima who in 1769 constructed this sequence as the number of moves of the outer ring in the optimal solution for the Chinese Rings puzzle[292]
1367 = safe prime,[60] balanced prime, sum of three, nine, and eleven consecutive primes (449 + 457 + 461, 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173, and 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151),[132]
1368 = number of edges in the join of two cycle graphs, both of order 36[175]
1369 = 372, centered octagonal number[216]
1370 = σ2(37): sum of squares of divisors of 37[293]
1371 = sum of the first 28 primes
1372 = Achilles number
1373 = number of lattice points inside a circle of radius 21[153]
1374 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,23}[147]
1375 = decagonal pyramidal number[294]
1376 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)[295]
1377 = maximal number of pieces that can be obtained by cutting an annulus with 51 cuts[152]
1378 = triangular number[66]
1379 = magic constant of n × n normal magic square and n-queens problem for n = 14.
1380 = number of 8-step mappings with 4 inputs[296]
1381 = centered pentagonal number[84] Mertens function zero
1382 = first 4 digit tetrachi number [297]
1383 = 3 × 461. 101383 + 7 is prime[298]
1384 =  [201]
1385 = up/down number[299]
1386 = octagonal pyramidal number[300]
1387 = 5th Fermat pseudoprime of base 2,[301] 22nd centered hexagonal number and the 19th decagonal number,[135] second Super-Poulet number.[302]
1388 = 4 × 192 - 3 × 19 + 1 and is therefore on the x-axis of Ulams spiral[303]
1389 = sum of first 42 composite numbers[212]
1390 = sum of first 43 nonprimes[244]
1391 = number of rational numbers which can be constructed from the set of integers between 1 and 47[185]
1392 = number of edges in the hexagonal triangle T(29)[155]
1393 = 7-Knödel number[163]
1394 = sum of totient function for first 67 integers
1395 = vampire number,[237] member of the Mian–Chowla sequence[56] triangular matchstick number[86]
1396 = centered triangular number[158]
1397 =  [304]
1398 = number of integer partitions of 40 whose distinct parts are connected[264]
1399 = emirp[305]

1400 to 1499 edit

1400 = number of sum-free subsets of {1, ..., 15}[306]
1401 = pinwheel number[131]
1402 = number of integer partitions of 48 whose augmented differences are distinct[307]
1403 = smallest x such that M(x) = 11, where M() is Mertens function[308]
1404 = heptagonal number[106]
1405 = 262 + 272, 72 + 82 + ... + 162, centered square number[53]
1406 = pronic number,[89] semi-meandric number[309]
1407 = 382 - 38 + 1 = H38 (the 38th Hogben number)[198]
1408 = maximal number of regions the plane is divided into by drawing 38 circles[238]
1409 = super-prime, Sophie Germain prime,[52] smallest number whose eighth power is the sum of 8 eighth powers, Proth prime[173]
1410 = denominator of the 46th Bernoulli number[310]
1411 = LS(41)[311]
1412 = LS(42),[311] spy number
1413 = LS(43)[311]
1414 = smallest composite that when added to sum of prime factors reaches a prime after 27 iterations[312]
1415 = the Mahonian number: T(8, 8)[221]
1416 = LS(46)[311]
1417 = number of partitions of 32 in which the number of parts divides 32[313]
1418 = smallest x such that M(x) = 13, where M() is Mertens function[308]
1419 = Zeisel number[314]
1420 = Number of partitions of 56 into prime parts
1421 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 29-manifold to be realizable as a sub-manifold,[315] spy number
1422 = number of partitions of 15 with two parts marked[316]
1423 = 200 + 1223 and the 200th prime is 1223[317] Also Used as a Hate symbol
1424 = number of nonnegative solutions to x2 + y2 ≤ 422[286]
1425 = self-descriptive number in base 5
1426 = sum of totient function for first 68 integers, pentagonal number,[111] number of strict partions of 42[143]
1427 = twin prime together with 1429[318]
1428 = number of complete ternary trees with 6 internal nodes, or 18 edges[319]
1429 = number of partitions of 53 such that the smallest part is greater than or equal to number of parts[257]
1430 = Catalan number[320]
1431 = triangular number,[66] hexagonal number[67]
1432 = member of Padovan sequence[112]
1433 = super-prime, Honaker prime,[258] typical port used for remote connections to Microsoft SQL Server databases
1434 = rounded volume of a regular tetrahedron with edge length 23[321]
1435 = vampire number;[237] the standard railway gauge in millimetres, equivalent to 4 feet 8+12 inches (1.435 m)
1436 = discriminant of a totally real cubic field[322]
1437 = smallest number of complexity 20: smallest number requiring 20 1's to build using +, * and ^[323]
1438 = k such that 5 × 2k - 1 is prime[275]
1439 = Sophie Germain prime,[52] safe prime[60]
1440 = a highly totient number[172] and a 481-gonal number. Also, the number of minutes in one day, the blocksize of a standard 3+1/2 floppy disk, and the horizontal resolution of WXGA(II) computer displays
1441 = star number[124]
1442 = number of parts in all partitions of 31 into distinct parts[83]
1443 = the sum of the second trio of three-digit permutable primes in decimal: 337, 373, and 733. Also the number of edges in the join of two cycle graphs, both of order 37[175]
1444 = 382, smallest pandigital number in Roman numerals
1445 =  [324]
1446 = number of points on surface of octahedron with edgelength 19[179]
1447 = super-prime, happy number
1448 = number k such that phi(prime(k)) is a square[325]
1449 = Stella octangula number
1450 = σ2(34): sum of squares of divisors of 34[293]
1451 = Sophie Germain prime[52]
1452 = first Zagreb index of the complete graph K12[326]
1453 = Sexy prime with 1459
1454 = 3 × 222 + 2 = number of points on surface of square pyramid of side-length 22[327]
1455 = k such that geometric mean of phi(k) and sigma(k) is an integer[328]
1456 = number of regions in regular 15-gon with all diagonals drawn[329]
1457 = 2 × 272 − 1 = a twin square[330]
1458 = maximum determinant of an 11 by 11 matrix of zeroes and ones, 3-smooth number (2×36)
1459 = Sexy prime with 1453, sum of nine consecutive primes (139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181), pierpont prime
1460 = The number of years that would have to pass in the Julian calendar in order to accrue a full year's worth of leap days.
1461 = number of partitions of 38 into prime power parts[241]
1462 = (35 - 1) × (35 + 8) = the first Zagreb index of the wheel graph with 35 vertices[331]
1463 = total number of parts in all partitions of 16[103]
1464 = rounded total surface area of a regular icosahedron with edge length 13[332]
1465 = 5-Knödel number[167]
1466 =  , where   = number of divisors of  [333]
1467 = number of partitions of 39 with zero crank[334]
1468 = number of polyhexes with 11 cells that tile the plane by translation[335]
1469 = octahedral number,[176] highly cototient number[81]
1470 = pentagonal pyramidal number,[336] sum of totient function for first 69 integers
1471 = super-prime, centered heptagonal number[107]
1472 = number of overpartitions of 15[337]
1473 = cropped hexagone[276]
1474 =  : triangular number plus quarter square (i.e., A000217(44) + A002620(44))[338]
1475 = number of partitions of 33 into parts each of which is used a different number of times[339]
1476 = coreful perfect number[340]
1477 = 7-Knödel number[163]
1478 = total number of largest parts in all compositions of 11[341]
1479 = number of planar partitions of 12[342]
1480 = sum of the first 29 primes
1481 = Sophie Germain prime[52]
1482 = pronic number,[89] number of unimodal compositions of 15 where the maximal part appears once[343]
1483 = 392 - 39 + 1 = H39 (the 39th Hogben number)[198]
1484 = maximal number of regions the plane is divided into by drawing 39 circles[238]
1485 = triangular number
1486 = number of strict solid partitions of 19[127]
1487 = safe prime[60]
1488 = triangular matchstick number[86]
1489 = centered triangular number[158]
1490 = tetranacci number[344]
1491 = nonagonal number,[213] Mertens function zero
1492 = discriminant of a totally real cubic field,[322] Mertens function zero
1493 = Stern prime[195]
1494 = sum of totient function for first 70 integers
1495 = 9###[345]
1496 = square pyramidal number[55]
1497 = skiponacci number[154]
1498 = number of flat partitions of 41[346]
1499 = Sophie Germain prime,[52] super-prime

1500 to 1599 edit

1500 = hypotenuse in three different Pythagorean triangles[347]
1501 = centered pentagonal number[84]
1502 = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 47[348]
1503 = least number of triangles of the Spiral of Theodorus to complete 12 revolutions[242]
1504 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)[295]
1505 = number of integer partitions of 41 with distinct differences between successive parts[349]
1506 = number of Golomb partitions of 28[350]
1507 = number of partitions of 32 that do not contain 1 as a part[72]
1508 = heptagonal pyramidal number[184]
1509 = pinwheel number[131]
1510 = deficient number, odious number
1511 = Sophie Germain prime,[52] balanced prime[132]
1512 = k such that geometric mean of phi(k) and sigma(k) is an integer[328]
1513 = centered square number[53]
1514 = sum of first 44 composite numbers[212]
1515 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 30-manifold to be realizable as a sub-manifold[315]
1516 =  [351]
1517 = number of lattice points inside a circle of radius 22[153]
1518 = sum of first 32 semiprimes,[352] Mertens function zero
1519 = number of polyhexes with 8 cells,[353] Mertens function zero
1520 = pentagonal number,[111] Mertens function zero, forms a Ruth–Aaron pair with 1521 under second definition
1521 = 392, Mertens function zero, centered octagonal number,[216] forms a Ruth–Aaron pair with 1520 under second definition
1522 = k such that 5 × 2k - 1 is prime[275]
1523 = super-prime, Mertens function zero, safe prime,[60] member of the Mian–Chowla sequence[56]
1524 = Mertens function zero, k such that geometric mean of phi(k) and sigma(k) is an integer[328]
1525 = heptagonal number,[106] Mertens function zero
1526 = number of conjugacy classes in the alternating group A27[354]
1527 = number of 2-dimensional partitions of 11,[355] Mertens function zero
1528 = Mertens function zero, rounded total surface area of a regular octahedron with edge length 21[356]
1529 = composite de Polignac number[208]
1530 = vampire number[237]
1531 = prime number, centered decagonal number, Mertens function zero
1532 = number of series-parallel networks with 9 unlabeled edges,[357] Mertens function zero
1533 = 21 × 73 = 21 × 21st prime[245]
1534 = number of achiral integer partitions of 50[288]
1535 = Thabit number
1536 = a common size of microplate, 3-smooth number (29×3), number of threshold functions of exactly 4 variables[358]
1537 = Keith number,[133] Mertens function zero
1538 = number of surface points on a cube with edge-length 17[57]
1539 = maximal number of pieces that can be obtained by cutting an annulus with 54 cuts[152]
1540 = triangular number, hexagonal number,[67] decagonal number,[135] tetrahedral number[150]
1541 = octagonal number[181]
1542 = k such that 2^k starts with k[359]
1543 = prime dividing all Fibonacci sequences,[360] Mertens function zero
1544 = Mertens function zero, number of partitions of integer partitions of 17 where all parts have the same length[361]
1545 = number of reversible string structures with 9 beads using exactly three different colors[362]
1546 = number of 5 X 5 binary matrices with at most one 1 in each row and column,[363] Mertens function zero
1547 = hexagonal pyramidal number
1548 = coreful perfect number[340]
1549 = de Polignac prime[364]
1550 =   = number of cards needed to build a 31-tier house of cards with a flat, one-card-wide roof[365]
1551 = 6920 - 5369 = A169952(24) - A169952(23) = A169942(24) = number of Golomb rulers of length 24[366][367]
1552 = Number of partitions of 57 into prime parts
1553 = 509 + 521 + 523 = a prime that is the sum of three consecutive primes[368]
1554 = 2 × 3 × 7 × 37 = product of four distinct primes[369]
15552 divides 61554[370]
1556 = sum of the squares of the first nine primes
1557 = number of graphs with 8 nodes and 13 edges[371]
1558 = number k such that k64 + 1 is prime
1559 = Sophie Germain prime[52]
1560 = pronic number[89]
1561 = a centered octahedral number,[180] number of series-reduced trees with 19 nodes[372]
1562 = maximal number of regions the plane is divided into by drawing 40 circles[238]
1563 =  [373]
1564 = sum of totient function for first 71 integers
1565 =   and  [374]
1566 = number k such that k64 + 1 is prime
1567 = number of partitions of 24 with at least one distinct part[232]
1568 = Achilles number[375]
1569 = 2 × 282 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 28[231]
1570 = 2 × 282 + 2 = number of points on surface of tetrahedron with edgelength 28[174]
1571 = Honaker prime[258]
1572 = member of the Mian–Chowla sequence[56]
1573 = discriminant of a totally real cubic field[322]
1574256 + 1 is prime[376]
1575 = odd abundant number,[377] sum of the nontriangular numbers between successive triangular numbers, number of partitions of 24[234]
157614 == 1 (mod 15^2)[378]
1577 = sum of the quadratic residues of 83[379]
1578 = sum of first 45 composite numbers[212]
1579 = number of partitions of 54 such that the smallest part is greater than or equal to number of parts[257]
1580 = number of achiral integer partitions of 51[288]
1581 = number of edges in the hexagonal triangle T(31)[155]
1582 = a number such that the integer triangle [A070080(1582), A070081(1582), A070082(1582)] has an integer area[380]
1583 = Sophie Germain prime
1584 = triangular matchstick number[86]
1585 = Riordan number, centered triangular number[158]
1586 = area of the 23rd conjoined trapezoid[202]
1587 = 3 × 232 = number of edges of a complete tripartite graph of order 69, K23,23,23[381]
1588 = sum of totient function for first 72 integers
1589 = composite de Polignac number[208]
1590 = rounded volume of a regular icosahedron with edge length 9[382]
1591 = rounded volume of a regular octahedron with edge length 15[256]
1592 = sum of all divisors of the first 36 odd numbers[383]
1593 = sum of the first 30 primes
1594 = minimal cost of maximum height Huffman tree of size 17[384]
1595 = number of non-isomorphic set-systems of weight 10
1596 = triangular number
1597 = Fibonacci prime,[385] Markov prime,[270] super-prime, emirp
1598 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,25}[147]
1599 = number of edges in the join of two cycle graphs, both of order 39[175]

1600 to 1699 edit

1600 = 402, structured great rhombicosidodecahedral number,[386] repdigit in base 7 (44447), street number on Pennsylvania Avenue of the White House, length in meters of a common High School Track Event, perfect score on SAT (except from 2005 to 2015)
1601 = Sophie Germain prime, Proth prime,[173] the novel 1601 (Mark Twain)
1602 = number of points on surface of octahedron with edgelength 20[179]
1603 = number of partitions of 27 with nonnegative rank[387]
1604 = number of compositions of 22 into prime parts[388]
1605 = number of polyominoes consisting of 7 regular octagons[389]
1606 = enneagonal pyramidal number[390]
1607 = member of prime triple with 1609 and 1613[391]
1608 =  [201]
1609 = cropped hexagonal number[276]
1610 = number of strict partions of 43[143]
1611 = number of rational numbers which can be constructed from the set of integers between 1 and 51[185]
1612 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 31-manifold to be realizable as a sub-manifold[315]
1613, 1607 and 1619 are all primes[392]
1614 = number of ways of refining the partition 8^1 to get 1^8[393]
1615 = composite number such that the square mean of its prime factors is a nonprime integer[394]
1616 =   = number of monotonic triples (x,y,z) in {1,2,...,16}3[395]
1617 = pentagonal number[111]
1618 = centered heptagonal number[107]
1619 = palindromic prime in binary, safe prime[60]
1620 = 809 + 811: sum of twin prime pair[224]
1621 = super-prime, pinwheel number[131]
1622 = semiprime of the form prime + 1[396]
1623 is not the sum of two triangular numbers and a fourth power[397]
1624 = number of squares in the Aztec diamond of order 28[398]
1625 = centered square number[53]
1626 = centered pentagonal number[84]
1627 = prime and 2 × 1627 - 1 = 3253 is also prime[399]
1628 = centered pentagonal number[84]
1629 = rounded volume of a regular tetrahedron with edge length 24[321]
1630 = number k such that k^64 + 1 is prime
1631 =  [400]
1632 = number of acute triangles made from the vertices of a regular 18-polygon[401]
1633 = star number[124]
1634 = Narcissistic number in base 10
1635 = number of partitions of 56 whose reciprocal sum is an integer[402]
1636 = number of nonnegative solutions to x2 + y2 ≤ 452[286]
1637 = prime island: least prime whose adjacent primes are exactly 30 apart[403]
1638 = harmonic divisor number,[404] 5 × 21638 - 1 is prime[275]
1639 = nonagonal number[213]
1640 = pronic number[89]
1641 = 412 - 41 + 1 = H41 (the 41st Hogben number)[198]
1642 = maximal number of regions the plane is divided into by drawing 41 circles[238]
1643 = sum of first 46 composite numbers[212]
1644 = 821 + 823: sum of twin prime pair[224]
1645 = number of 16-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection[405]
1646 = number of graphs with 8 nodes and 14 edges[371]
1647 and 1648 are both divisible by cubes[406]
1648 = number of partitions of 343 into distinct cubes[407]
1649 = highly cototient number,[81] Leyland number[150]
1650 = number of cards to build an 33-tier house of cards[197]
1651 = heptagonal number[106]
1652 = number of partitions of 29 into a prime number of parts[145]
1653 = triangular number, hexagonal number,[67] number of lattice points inside a circle of radius 23[153]
1654 = number of partitions of 42 into divisors of 42[408]
1655 = rounded volume of a regular dodecahedron with edge length 6[409]
1656 = 827 + 829: sum of twin prime pair[224]
1657 = cuban prime,[410] prime of the form 2p-1
1658 = smallest composite that when added to sum of prime factors reaches a prime after 25 iterations[312]
1659 = number of rational numbers which can be constructed from the set of integers between 1 and 52[185]
1660 = sum of totient function for first 73 integers
1661 = 11 × 151, palindrome that is a product of two palindromic primes[141]
1662 = number of partitions of 49 into pairwise relatively prime parts[194]
1663 = a prime number and 51663 - 41663 is a 1163-digit prime number[411]
1664 = k such that k, k+1 and k+2 are sums of 2 squares[412]
1665 = centered tetrahedral number[271]
1666 = largest efficient pandigital number in Roman numerals (each symbol occurs exactly once)
1667 = 228 + 1439 and the 228th prime is 1439[317]
1668 = number of partitions of 33 into parts all relatively prime to 33[413]
1669 = super-prime, smallest prime with a gap of exactly 24 to the next prime[414]
1670 = number of compositions of 12 such that at least two adjacent parts are equal[415]
1671 divides the sum of the first 1671 composite numbers[416]
1672 = 412 - 32, the only way to express 1672 as a difference of prime squares[277]
1673 = RMS number[417]
1674 = k such that geometric mean of phi(k) and sigma(k) is an integer[328]
1675 = Kin number[418]
1676 = number of partitions of 34 into parts each of which is used a different number of times[339]
1677 = 412 - 22, the only way to express 1677 as a difference of prime squares[277]
1678 = n such that n32 + 1 is prime[164]
1679 = highly cototient number,[81] semiprime (23 × 73, see also Arecibo message), number of parts in all partitions of 32 into distinct parts[83]
1680 = highly composite number,[236] number of edges in the join of two cycle graphs, both of order 40[175]
1681 = 412, smallest number yielded by the formula n2 + n + 41 that is not a prime; centered octagonal number[216]
1682 = and 1683 is a member of a Ruth–Aaron pair (first definition)
1683 = triangular matchstick number[86]
1684 = centered triangular number[158]
1685 = 5-Knödel number[167]
1686 =  [201]
1687 = 7-Knödel number[163]
1688 = number of finite connected sets of positive integers greater than one with least common multiple 72[419]
1689 =  [420]
1690 = number of compositions of 14 into powers of 2[421]
1691 = the same upside down, which makes it a strobogrammatic number[422]
1692 = coreful perfect number[340]
1693 = smallest prime > 412.[182]
1694 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,26}[147]
1695 = magic constant of n × n normal magic square and n-queens problem for n = 15. Number of partitions of 58 into prime parts
1696 = sum of totient function for first 74 integers
1697 = Friedlander-Iwaniec prime[139]
1698 = number of rooted trees with 47 vertices in which vertices at the same level have the same degree[240]
1699 = number of rooted trees with 48 vertices in which vertices at the same level have the same degree[240]

1700 to 1799 edit

1700 = σ2(39): sum of squares of divisors of 39[293]
1701 =  , decagonal number, hull number of the U.S.S. Enterprise on Star Trek
1702 = palindromic in 3 consecutive bases: 89814, 78715, 6A616
1703 = 1703131131 / 1000077 and the divisors of 1703 are 1703, 131, 13 and 1[423]
1704 = sum of the squares of the parts in the partitions of 18 into two distinct parts[424]
1705 = tribonacci number[425]
1706 = 1 + 4 + 16 + 64 + 256 + 1024 + 256 + 64 + 16 + 4 + 1 sum of fifth row of triangle of powers of 4[426]
1707 = number of partitions of 30 in which the number of parts divides 30[313]
1708 = 22 × 7 × 61 a number whose product of prime indices 1 × 1 × 4 × 18 is divisible by its sum of prime factors 2 + 2 + 7 + 61[427]
1709 = first of a sequence of eight primes formed by adding 57 in the middle. 1709, 175709, 17575709, 1757575709, 175757575709, 17575757575709, 1757575757575709 and 175757575757575709 are all prime, but 17575757575757575709 = 232433 × 75616446785773
1710 = maximal number of pieces that can be obtained by cutting an annulus with 57 cuts[152]
1711 = triangular number, centered decagonal number
1712 = number of irredundant sets in the 29-cocktail party graph[246]
1713 = number of aperiodic rooted trees with 12 nodes[428]
1714 = number of regions formed by drawing the line segments connecting any two of the 18 perimeter points of an 3 × 6 grid of squares[429]
1715 = k such that geometric mean of phi(k) and sigma(k) is an integer[328]
1716 = 857 + 859: sum of twin prime pair[224]
1717 = pentagonal number[111]
1718 =  [430]
1719 = composite de Polignac number[208]
1720 = sum of the first 31 primes
1721 = twin prime; number of squares between 422 and 424.[149]
1722 = Giuga number,[431] pronic number[89]
1723 = super-prime
1724 = maximal number of regions the plane is divided into by drawing 42 circles[238]
1725 = 472 - 222 = (prime(15))2 - (nonprime(15))2[432]
1726 = number of partitions of 44 into distinct and relatively prime parts[433]
1727 = area of the 24th conjoined trapezoid[202]
1728 = the quantity expressed as 1000 in duodecimal, that is, the cube of twelve (called a great gross), and so, the number of cubic inches in a cubic foot, palindromic in base 11 (133111) and 23 (36323)
1729 = taxicab number, Carmichael number, Zeisel number, centered cube number, Hardy–Ramanujan number. In the decimal expansion of e the first time all 10 digits appear in sequence starts at the 1729th digit (or 1728th decimal place). In 1979 the rock musical Hair closed on Broadway in New York City after 1729 performances. Palindromic in bases 12, 32, 36.
1730 = 3 × 242 + 2 = number of points on surface of square pyramid of side-length 24[327]
1731 = k such that geometric mean of phi(k) and sigma(k) is an integer[328]
1732 =  [434]
1733 = Sophie Germain prime, palindromic in bases 3, 18, 19.
1734 = surface area of a cube of edge length 17[435]
1735 = number of partitions of 55 such that the smallest part is greater than or equal to number of parts[257]
1736 = sum of totient function for first 75 integers, number of surface points on a cube with edge-length 18[57]
1737 = pinwheel number[131]
1738 = number of achiral integer partitions of 52[288]
1739 = number of 1s in all partitions of 30 into odd parts[436]
1740 = number of squares in the Aztec diamond of order 29[398]
1741 = super-prime, centered square number[53]
1742 = number of regions the plane is divided into by 30 ellipses[137]
1743 = wiener index of the windmill graph D(3,21)[161]
1744 = k such that k, k+1 and k+2 are sums of 2 squares[412]
1745 = 5-Knödel number[167]
1746 = number of unit-distance graphs on 8 nodes[437]
1747 = balanced prime[132]
1748 = number of partitions of 55 into distinct parts in which the number of parts divides 55[438]
1749 = number of integer partitions of 33 with no part dividing all the others[262]
1750 = hypotenuse in three different Pythagorean triangles[347]
1751 = cropped hexagone[276]
1752 = 792 - 672, the only way to express 1752 as a difference of prime squares[277]
1753 = balanced prime[132]
1754 = k such that 5*2k - 1 is prime[275]
1755 = number of integer partitions of 50 whose augmented differences are distinct[307]
1756 = centered pentagonal number[84]
1757 = least number of triangles of the Spiral of Theodorus to complete 13 revolutions[242]
1758 =  [201]
1759 = de Polignac prime[364]
1760 = the number of yards in a mile
1761 = k such that k, k+1 and k+2 are products of two primes[278]
1762 = number of binary sequences of length 12 and curling number 2[439]
1763 = number of edges in the join of two cycle graphs, both of order 41[175]
1764 = 422
1765 = number of stacks, or planar partitions of 15[440]
1766 = number of points on surface of octahedron with edgelength 21[179]
1767 = σ(282) = σ(352)[441]
1768 = number of nonequivalent dissections of an hendecagon into 8 polygons by nonintersecting diagonals up to rotation[442]
1769 = maximal number of pieces that can be obtained by cutting an annulus with 58 cuts[152]
1770 = triangular number, hexagonal number,[67] Seventeen Seventy, town in Australia
1771 = tetrahedral number[150]
1772 = centered heptagonal number,[107] sum of totient function for first 76 integers
1773 = number of words of length 5 over the alphabet {1,2,3,4,5} such that no two even numbers appear consecutively[443]
1774 = number of rooted identity trees with 15 nodes and 5 leaves[444]
1775 =  : sum of piles of first 10 primes[445]
1776 = square star number.[446] The number of pieces that could be seen in a 7 × 7 × 7× 7 Rubik's Tesseract.
1777 = smallest prime > 422.[182]
1778 = least k >= 1 such that the remainder when 6k is divided by k is 22[447]
1779 = number of achiral integer partitions of 53[288]
1780 = number of lattice paths from (0, 0) to (7, 7) using E (1, 0) and N (0, 1) as steps that horizontally cross the diagonal y = x with even many times[448]
1781 = the first 1781 digits of e form a prime[449]
1782 = heptagonal number[106]
1783 = de Polignac prime[364]
1784 = number of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} such that every pair of distinct elements has a different quotient[450]
1785 = square pyramidal number,[55] triangular matchstick number[86]
1786 = centered triangular number[158]
1787 = super-prime, sum of eleven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191)
1788 = Euler transform of -1, -2, ..., -34[451]
1789 = number of wiggly sums adding to 17 (terms alternately increase and decrease or vice versa)[452]
1790 = number of partitions of 50 into pairwise relatively prime parts[194]
1791 = largest natural number that cannot be expressed as a sum of at most four hexagonal numbers.
1792 = Granville number
1793 = number of lattice points inside a circle of radius 24[153]
1794 = nonagonal number,[213] number of partitions of 33 that do not contain 1 as a part[72]
1795 = number of heptagons with perimeter 38[453]
1796 = k such that geometric mean of phi(k) and sigma(k) is an integer[328]
1797 = number k such that phi(prime(k)) is a square[325]
1798 = 2 × 29 × 31 = 102 × 111012 × 111112, which yield zero when the prime factors are xored together[454]
1799 = 2 × 302 − 1 = a twin square[330]

1800 to 1899 edit

1800 = pentagonal pyramidal number,[336] Achilles number, also, in da Ponte's Don Giovanni, the number of women Don Giovanni had slept with so far when confronted by Donna Elvira, according to Leporello's tally
1801 = cuban prime, sum of five and nine consecutive primes (349 + 353 + 359 + 367 + 373 and 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227)[410]
1802 = 2 × 302 + 2 = number of points on surface of tetrahedron with edgelength 30,[174] number of partitions of 30 such that the number of odd parts is a part[206]
1803 = number of decahexes that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion)[455]
1804 = number k such that k^64 + 1 is prime
1805 = number of squares between 432 and 434.[149]
1806 = pronic number,[89] product of first four terms of Sylvester's sequence, primary pseudoperfect number,[456] only number for which n equals the denominator of the nth Bernoulli number,[457] Schröder number[458]
1807 = fifth term of Sylvester's sequence[459]
1808 = maximal number of regions the plane is divided into by drawing 43 circles[238]
1809 = sum of first 17 super-primes[460]
1810 =  [461]
1811 = Sophie Germain prime
1812 = n such that n32 + 1 is prime[164]
1813 = number of polyominoes with 26 cells, symmetric about two orthogonal axes[462]
1814 = 1 + 6 + 36 + 216 + 1296 + 216 + 36 + 6 + 1 = sum of 4th row of triangle of powers of six[463]
1815 = polygonal chain number  [464]
1816 = number of strict partions of 44[143]
1817 = total number of prime parts in all partitions of 20[465]
1818 = n such that n32 + 1 is prime[164]
1819 = sum of the first 32 primes, minus 32[466]
1820 = pentagonal number,[111] pentatope number,[291] number of compositions of 13 whose run-lengths are either weakly increasing or weakly decreasing[467]
1821 = member of the Mian–Chowla sequence[56]
1822 = number of integer partitions of 43 whose distinct parts are connected[264]
1823 = super-prime, safe prime[60]
1824 = 432 - 52, the only way to express 1824 as a difference of prime squares[277]
1825 = octagonal number[181]
1826 = decagonal pyramidal number[294]
1827 = vampire number[237]
1828 = meandric number, open meandric number, appears twice in the first 10 decimal digits of e
1829 = composite de Polignac number[208]
1830 = triangular number
1831 = smallest prime with a gap of exactly 16 to next prime (1847)[468]
1832 = sum of totient function for first 77 integers
1833 = number of atoms in a decahedron with 13 shells[469]
1834 = octahedral number,[176] sum of the cubes of the first five primes
1835 = absolute value of numerator of  [470]
1836 = factor by which a proton is more massive than an electron
1837 = star number[124]
1838 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,27}[147]
1839 =  [471]
1840 = 432 - 32, the only way to express 1840 as a difference of prime squares[277]
1841 = solution to the postage stamp problem with 3 denominations and 29 stamps,[472] Mertens function zero
1842 = number of unlabeled rooted trees with 11 nodes[473]
1843 = k such that phi(k) is a perfect cube,[474] Mertens function zero
1844 = 37 - 73,[475] Mertens function zero
1845 = number of partitions of 25 containing at least one prime,[476] Mertens function zero
1846 = sum of first 49 composite numbers[212]
1847 = super-prime
1848 = number of edges in the join of two cycle graphs, both of order 42[175]
1849 = 432, palindromic in base 6 (= 123216), centered octagonal number[216]
1850 = Number of partitions of 59 into prime parts
1851 = sum of the first 32 primes
1852 = number of quantales on 5 elements, up to isomorphism[477]
1853 = sum of primitive roots of 27-th prime,[478] Mertens function zero
1854 = number of permutations of 7 elements with no fixed points,[479] Mertens function zero
1855 = rencontres number: number of permutations of [7] with exactly one fixed point[480]
1856 = sum of totient function for first 78 integers
1857 = Mertens function zero, pinwheel number[131]
1858 = number of 14-carbon alkanes C14H30 ignoring stereoisomers[481]
1859 = composite de Polignac number[208]
1860 = number of squares in the Aztec diamond of order 30[482]
1861 = centered square number,[53] Mertens function zero
1862 = Mertens function zero, forms a Ruth–Aaron pair with 1863 under second definition
1863 = Mertens function zero, forms a Ruth–Aaron pair with 1862 under second definition
1864 = Mertens function zero,   is a prime[483]
1865 = 123456: Largest senary metadrome (number with digits in strict ascending order in base 6)[484]
1866 = Mertens function zero, number of plane partitions of 16 with at most two rows[485]
1867 = prime de Polignac number[364]
1868 = smallest number of complexity 21: smallest number requiring 21 1's to build using +, * and ^[323]
1869 = Hultman number: SH(7, 4)[486]
1870 = decagonal number[135]
1871 = the first prime of the 2 consecutive twin prime pairs: (1871, 1873) and (1877, 1879)[487]
1872 = first Zagreb index of the complete graph K13[326]
1873 = number of Narayana's cows and calves after 21 years[247]
1874 = area of the 25th conjoined trapezoid[202]
1875 = 502 - 252
1876 = number k such that k^64 + 1 is prime
1877 = number of partitions of 39 where 39 divides the product of the parts[488]
1878 = n such that n32 + 1 is prime[164]
1879 = a prime with square index[489]
1880 = the 10th element of the self convolution of Lucas numbers[490]
1881 = tricapped prism number[491]
1882 = number of linearly separable Boolean functions in 4 variables[492]
1883 = number of conjugacy classes in the alternating group A28[354]
1884 = k such that 5*2k - 1 is prime[275]
1885 = Zeisel number[314]
1886 = number of partitions of 64 into fourth powers[493]
1887 = number of edges in the hexagonal triangle T(34)[155]
1888 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)[295]
1889 = Sophie Germain prime, highly cototient number[81]
1890 = triangular matchstick number[86]
1891 = triangular number, hexagonal number,[67] centered pentagonal number,[84] centered triangular number[158]
1892 = pronic number[89]
1893 = 442 - 44 + 1 = H44 (the 44th Hogben number)[198]
1894 = maximal number of regions the plane is divided into by drawing 44 circles[238]
1895 = Stern-Jacobsthal number[282]
1896 = member of the Mian-Chowla sequence[56]
1897 = member of Padovan sequence,[112] number of triangle-free graphs on 9 vertices[494]
1898 = smallest multiple of n whose digits sum to 26[495]
1899 = cropped hexagone[276]

1900 to 1999 edit

1900 = number of primes <= 214.[63] Also 1900 (film) or Novecento, 1976 movie. 1900 was the year Thorold Gosset introduced his list of semiregular polytopes; it is also the year Max Brückner published his study of polyhedral models, including stellations of the icosahedron, such as the novel final stellation of the icosahedron.
1901 = Sophie Germain prime, centered decagonal number
1902 = number of symmetric plane partitions of 27[496]
1903 = generalized catalan number[497]
1904 = number of flat partitions of 43[346]
1905 = Fermat pseudoprime[136]
1906 = number n such that 3n - 8 is prime[498]
1907 = safe prime,[60] balanced prime[132]
1908 = coreful perfect number[340]
1909 = hyperperfect number[499]
1910 = number of compositions of 13 having exactly one fixed point[500]
1911 = heptagonal pyramidal number[184]
1912 = size of 6th maximum raising after one blind in pot-limit poker[501]
1913 = super-prime, Honaker prime[258]
1914 = number of bipartite partitions of 12 white objects and 3 black ones[502]
1915 = number of nonisomorphic semigroups of order 5[503]
1916 = sum of first 50 composite numbers[212]
1917 = number of partitions of 51 into pairwise relatively prime parts[194]
1918 = heptagonal number[106]
1919 = smallest number with reciprocal of period length 36 in base 10[504]
1920 = sum of the nontriangular numbers between successive triangular numbers
1921 = 4-dimensional centered cube number[505]
1922 = Area of a square with diagonal 62[92]
1923 = 2 × 312 + 1 = number of different 2 X 2 determinants with integer entries from 0 to 31[231]
1924 = 2 × 312 + 2 = number of points on surface of tetrahedron with edgelength 31[174]
1925 = number of ways to write 24 as an orderless product of orderless sums[144]
1926 = pentagonal number[111]
1927 = 211 - 112[506]
1928 = number of distinct values taken by 2^2^...^2 (with 13 2's and parentheses inserted in all possible ways)[507]
1929 = Mertens function zero, number of integer partitions of 42 whose distinct parts are connected[264]
1930 = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 53[348]
1931 = Sophie Germain prime
1932 = number of partitions of 40 into prime power parts[241]
1933 = centered heptagonal number,[107] Honaker prime[258]
1934 = sum of totient function for first 79 integers
1935 = number of edges in the join of two cycle graphs, both of order 43[175]
1936 = 442, 18-gonal number,[508] 324-gonal number.
1937 = number of chiral n-ominoes in 12-space, one cell labeled[509]
1938 = Mertens function zero, number of points on surface of octahedron with edgelength 22[179]
1939 = 7-Knödel number[163]
1940 = the Mahonian number: T(8, 9)[221]
1941 = maximal number of regions obtained by joining 16 points around a circle by straight lines[510]
1942 = number k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes[511]
1943 = largest number not the sum of distinct tetradecagonal numbers[512]
1944 = 3-smooth number (23×35), Achilles number[375]
1945 = number of partitions of 25 into relatively prime parts such that multiplicities of parts are also relatively prime[513]
1946 = number of surface points on a cube with edge-length 19[57]
1947 = k such that 5·2k + 1 is a prime factor of a Fermat number 22m + 1 for some m[514]
1948 = number of strict solid partitions of 20[127]
1949 = smallest prime > 442.[182]
1950 =  ,[515] largest number not the sum of distinct pentadecagonal numbers[512]
1951 = cuban prime[410]
1952 = number of covers of {1, 2, 3, 4}[516]
1953 = triangular number
1954 = number of sum-free subsets of {1, ..., 16}[306]
1955 = number of partitions of 25 with at least one distinct part[232]
1956 = nonagonal number[213]
1957 =   = total number of ordered k-tuples (k=0,1,2,3,4,5,6) of distinct elements from an 6-element set[517]
1958 = number of partitions of 25[234]
1959 = Heptanacci-Lucas number[518]
1960 = number of parts in all partitions of 33 into distinct parts[83]
1961 = number of lattice points inside a circle of radius 25[153]
1962 = number of edges in the join of the complete graph K36 and the cycle graph C36[519]
1963! - 1 is prime[520]
1964 = number of linear forests of planted planar trees with 8 nodes[521]
1965 = total number of parts in all partitions of 17[103]
1966 = sum of totient function for first 80 integers
1967 = least edge-length of a square dissectable into at least 30 squares in the Mrs. Perkins's quilt problem[522]
σ(1968) = σ(1967) + σ(1966)[523]
1969 = Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize[524]
1970 = number of compositions of two types of 9 having no even parts[525]
1971 =  [526]
1972 = n such that   is prime[527]
1973 = Sophie Germain prime, Leonardo prime
1974 = number of binary vectors of length 17 containing no singletons[214]
1975 = number of partitions of 28 with nonnegative rank[387]
1976 = octagonal number[181]
1977 = number of non-isomorphic multiset partitions of weight 9 with no singletons[528]
1978 = n such that n | (3n + 5)[529]
1979 = number of squares between 452 and 454.[149]
1980 = pronic number[89]
1981 = pinwheel number[131]
1982 = maximal number of regions the plane is divided into by drawing 45 circles[238]
1983 = skiponacci number[154]
1984 = 11111000000 in binary, see also: 1984 (disambiguation)
1985 = centered square number[53]
1986 = number of ways to write 25 as an orderless product of orderless sums[144]
1987 = 300th prime number
1988 = sum of the first 33 primes
1989 = number of 9-step mappings with 4 inputs[296]
1990 = Stella octangula number
1991 = 11 × 181, the 46th Gullwing number,[530] palindromic composite number with only palindromic prime factors[531]
1992 = number of nonisomorphic sets of nonempty subsets of a 4-set[532]
1993 = a number with the property that 41993 - 31993 is prime,[533] number of partitions of 30 into a prime number of parts[145]
1994 = Glaisher's function W(37)[534]
1995 = number of unlabeled graphs on 9 vertices with independence number 6[535]
1996 = a number with the property that (1996! + 3)/3 is prime[536]
1997 =  [537]
1998 = triangular matchstick number[86]
1999 = centered triangular number[538] number of regular forms in a myriagram.

Prime numbers edit

There are 135 prime numbers between 1000 and 2000:[539][540]

1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999

Notes edit

  1. ^ 1000 is the fourth Wiener index of the grid   where   is the path graph on four vertices.[7] A connected graph with a given Wiener index represents the sum of the distances between all unordered pairs of vertices in said graph.
  2. ^ In the sequence of regular 1000-gonal numbers of the form  , the first non-trivial solution is 2997.[13] In Chowla's function, that counts the sum of divisors except for   and  , 2997 is the first number to have a value of 1600,[15] which is the Euler totient of 4000 and 6000,[16] while the fifth member in the sequence 9985 (that follows 0, 1, 1000, 2997 and 5992)[13] has an average of divisors that is 2997;[17][18] with 5992 ÷ 2 = 2996, and 1000 + 2997 + 5992 = 9989 (a difference of 4 from the fourth member, after 1).
    There are 499 regular star polygrams to the regular chiliagon: 300 are regular compound star forms — a count that represents the twenty-fourth triangular number[19] — with the remaining 199 forms represented by simple regular star polygons.
  3. ^ 1600, a repdigit in septenary (44447),[23] is the composite index of 1891, in turn the like-index of 2223.[22]
    2222 and 8888 are both numbers n such that n − 1 is prime (as with 4, 44, 444, and 888),[24] yielding respectively the 331st and 1107th prime numbers,[25] where the former (2221) is also the 64th super-prime.[26] These two prime indexes collectively have a range of 777 integers (1107 : 331), which as a number is also a repdigit in senary.[27]
  4. ^ The sum (2 + 3 + 5 + ... + 29) of the first 10 prime numbers is 129, which is the 97th indexed composite number.[29][22] 9973 is also the 201st super-prime,[26] where 1000 − 201 = 799, which is the smallest number in decimal to have a digit sum of 25,[30] and the mirror permutation of digits of 997.
    When splitting four-digit 9973 into two two-digit numbers, 99 and 73, the latter is the composite index of 99, that, when added together is 172, the one hundred and thirty-second composite, with 132 itself the 99th composite;[22] 73 is the twenty-first prime number.[25]
    1601 is the 252nd prime,[25] itself a value with a composite index of 197,[22] where 1601 is the 40th and largest consecutive prime lucky number of Euler of the form n2 + n + 41.[31][32] The number of 4-digit prime numbers, in decimal, is its mirror permutation of digits 1061, the 172nd prime.[33]
    Also, 7, 97 and 997 are all three respectively at a difference of 3 from 10, 100 and 1000, where, on the other hand, 9973 is 27 = 33 away from 10000.
    Note, that 8 as a binary number is "1000",[34] and this representation, when written in factorial base, is equivalent to 2410.[35] In primorial base, it is equal to 3010.[36]

References edit

  1. ^ "chiliad". Merriam-Webster. Archived from the original on 25 March 2022.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A051876 (24-gonal numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 30 November 2022.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A316729 (Generalized 30-gonal (or triacontagonal) numbers: m*(14*m - 13) with m equal to 0, +1, -1, +2, -2, +3, -3, ...)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A034828 (a(n) equal to floor(n^2/4)*(n/2).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
  5. ^ Ngaokrajang, Kival. Sloane, N. J. A. (ed.). "Illustration for n equal to 1..10 [A034828]". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Janjic, M.; Petkovic, B. (2013). "A Counting Function". pp. 14, 15. arXiv:1301.4550 [math.CO]. Bibcode:2013arXiv1301.4550J
  7. ^ Sloane, N. J. A. (ed.). "Sequence A143945 (Wiener index of the grid P_n x P_n, where P_n is the path graph on n vertices.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A054501 (Multiplicity sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A054500 (Indicator sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A054502 (Counting sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
  11. ^ I. Rivin, I. Vardi and P. Zimmermann (1994). The n-queens problem. American Mathematical Monthly. Washington, D.C.: Mathematical Association of America. 101 (7): 629–639. doi:10.1080/00029890.1994.11997004 JSTOR 2974691
  12. ^ Sloane, N. J. A. (ed.). "Sequence A364349 (Number of strict integer partitions of n containing the sum of no subset of the parts.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
  13. ^ a b c Sloane, N. J. A. (ed.). "Sequence A195163 (1000-gonal numbers: a(n) equal to n*(499*n - 498).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
  14. ^ Aṣiru, Muniru A. (2016). "All square chiliagonal numbers". International Journal of Mathematical Education in Science and Technology. Oxfordshire: Taylor & Francis. 47 (7): 1123–1134. Bibcode:2016IJMES..47.1123A. doi:10.1080/0020739X.2016.1164346. MR 3528540. S2CID 123953958. Zbl 1396.97005.
  15. ^ Sloane, N. J. A. (ed.). "Sequence A048050 (Chowla's function: sum of divisors of n except for 1 and n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
  16. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A000010 (Euler totient function phi(n): count numbers less than or equal to n and prime to n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A003601 (Numbers n such that the average of the divisors of n is an integer: sigma_0(n) divides sigma_1(n).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 16 July 2023.
  18. ^ Sloane, N. J. A. (ed.). "Sequence A102187 (Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 16 July 2023.
  19. ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers: a(n) is the binomial(n+1,2): n*(n+1)/2 equal to 0 + 1 + 2 + ... + n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
  20. ^ Sloane, N. J. A. (ed.). "Sequence A002322 (Reduced totient function psi(n): least k such that x^k is congruent 1 (mod n) for all x prime to n; also known as the Carmichael lambda function (exponent of unit group mod n); also called the universal exponent of n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
  21. ^ Sloane, N. J. A. (ed.). "Sequence A002088 (Sum of totient function: a(n) is Sum_{k equal to1..n} phi(k), cf. A000010.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
  22. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
  23. ^ Sloane, N. J. A. (ed.). "Sequence A048332 (Numbers that are repdigits in base 7.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A028987 (Repdigit - 1 is prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
  25. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 19 December 2023.
  26. ^ a b Sloane, N. J. A. (ed.). "Sequence A006450 (Prime-indexed primes: primes with prime subscripts.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 19 December 2023.
  27. ^ Sloane, N. J. A. (ed.). "Sequence A048331 (Numbers that are repdigits in base 6.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
  28. ^ Sloane, N. J. A. (ed.). "Sequence A366581 (a(n) equal to phi(p(n)), where phi is Euler's totient function (A000010) and p(n) is the number of partitions of n (A000041).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
  29. ^ Sloane, N. J. A. (ed.). "Sequence A127337 (Numbers that are the sum of 10 consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
  30. ^ Sloane, N. J. A. (ed.). "Sequence A051885 (Smallest number whose sum of digits is n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 20 December 2023.
  31. ^ Sloane, N. J. A. (ed.). "Sequence A202018 (a(n) equal to n^2 + n + 41.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 December 2023.
  32. ^ Sloane, N. J. A. (ed.). "Sequence A005846 (Primes of the form n^2 + n + 41.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 December 2023.
  33. ^ Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
  34. ^ Sloane, N. J. A. (ed.). "Sequence A007088 (The binary numbers (or binary words, or binary vectors, or binary expansion of n): numbers written in base 2.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
  35. ^ Sloane, N. J. A. (ed.). "Sequence A007623 (Integers written in factorial base.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 December 2023.
  36. ^ Sloane, N. J. A. (ed.). "Sequence A049345 (n written in primorial base.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 21 January 2024.
  37. ^ "1000". Prime Curious!. Archived from the original on 25 March 2022.
  38. ^ Sloane, N. J. A. (ed.). "Sequence A152396 (Let f(M,k) denote the decimal concatenation of k numbers starting with M: M | M-1 | M-2 | ... | M-k+1, k greater than 1. Then a(n) is the smallest M such that for all m in {1,..,n} an m-th prime occurs as f(M,k) for the smallest possible k, order prioritized m equal to 1 through n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 December 2023.
  39. ^ Sloane, N. J. A. (ed.). "Sequence A227949 (Primes obtained by concatenating decremented numbers starting at a power of 10.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 December 2023.
  40. ^ Ronan, Mark (2006). Symmetry and the Monster: One of the Greatest Quests of Mathematics. New York: Oxford University Press. pp. vii, 1–255. doi:10.1007/s00283-008-9007-9. ISBN 978-0-19-280722-9. MR 2215662. OCLC 180766312. Zbl 1113.00002.
  41. ^ Sloane, N. J. A. (ed.). "Sequence A001228 (Orders of sporadic simple groups.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 18 December 2023.
  42. ^ Sloane, N. J. A. (ed.). "Sequence A122189 (Heptanacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 13 July 2017.
  43. ^ Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 24 May 2022.
  44. ^ Sloane, N. J. A. (ed.). "Sequence A332307 (Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n grid graph)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 8 January 2023.
  45. ^ Sloane, N. J. A. (ed.). "Sequence A036063 (Increasing gaps among twin primes: size)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 8 January 2023.
  46. ^ a b Sloane, N. J. A. (ed.). "Sequence A003352 (Numbers that are the sum of 7 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
  47. ^ Sloane, N. J. A. (ed.). "Sequence A061341 (A061341 Numbers not ending in 0 whose cubes are concatenations of other cubes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 8 January 2023.
  48. ^ Sloane, N. J. A. (ed.). "Sequence A003353 (Numbers that are the sum of 8 positive 5th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
  49. ^ Sloane, N. J. A. (ed.). "Sequence A034262 (a(n) = n^3 + n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 24 May 2022.
  50. ^ a b Sloane, N. J. A. (ed.). "Sequence A020473 (Egyptian fractions: number of partitions of 1 into reciprocals of positive integers < n+1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 24 May 2022.
  51. ^ Sloane, N. J. A. (ed.). "Sequence A046092 (4 times triangular numbers: a(n) = 2*n*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
  52. ^ a b c d e f g h i j k l m n o Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes p: 2p+1 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  53. ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  54. ^ Sloane, N. J. A. (ed.). "Sequence A000325 (2^n - n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 24 May 2022.
  55. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  56. ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  57. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A005897 (6*n^2 + 2 for n > 0)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  58. ^ Sloane, N. J. A. (ed.). "Sequence A316729 (Generalized 30-gonal (or triacontagonal) numbers: m*(14*m - 13) with m = 0, +1, -1, +2, -2, +3, -3)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
  59. ^ Sloane, N. J. A. (ed.). "Sequence A006313 (Numbers n such that n^16 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 24 May 2022.
  60. ^ a b c d e f g h i j k l Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes p: (p-1)/2 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  61. ^ Sloane, N. J. A. (ed.). "Sequence A034964 (Sums of five consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 1 November 2022.
  62. ^ Sloane, N. J. A. (ed.). "Sequence A000162 (Number of 3-dimensional polyominoes (or polycubes) with n cells.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 1 November 2022.
  63. ^ a b Sloane, N. J. A. (ed.). "Sequence A007053 (Number of primes < 2^n+1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
  64. ^ Sloane, N. J. A. (ed.). "Sequence A004023 (Indices of prime repunits: numbers n such that 11...111 (with n 1's)... is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 25 February 2023.
  65. ^ Sloane, N. J. A. (ed.). "Sequence A004801 (Sum of 12 positive 9th powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
  66. ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  67. ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  68. ^ a b Sloane, N. J. A. (ed.). "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  69. ^ Sloane, N. J. A. (ed.). "Sequence A161328 (E-toothpick sequence (see Comments lines for definition))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
  70. ^ Sloane, N. J. A. (ed.). "Sequence A023036 (Smallest positive even integer that is an unordered sum of two primes in exactly n ways)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
  71. ^ Sloane, N. J. A. (ed.). "Sequence A007522 (Primes of the form 8n+7, that is, primes congruent to -1 mod 8)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
  72. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
  73. ^ a b Sloane, N. J. A. (ed.). "Sequence A000695 (Moser-de Bruijn sequence: sums of distinct powers of 4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 October 2023.
  74. ^ "A003356 - Oeis".
  75. ^ a b "A003357 - Oeis".
  76. ^ "A036301 - Oeis".
  77. ^ "A000567 - Oeis".
  78. ^ "A000025 - Oeis".
  79. ^ "A336130 - Oeis".
  80. ^ "A073576 - Oeis".
  81. ^ a b c d e f g "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 10 June 2016. Retrieved 12 June 2016.
  82. ^ "Base converter | number conversion".
  83. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A015723 (Number of parts in all partitions of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  84. ^ a b c d e f g h i "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 10 June 2016. Retrieved 12 June 2016.
  85. ^ "A003365 - Oeis".
  86. ^ a b c d e f g h i j k Sloane, N. J. A. (ed.). "Sequence A045943 (Triangular matchstick numbers: 3*n*(n+1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
  87. ^ "A005448 - Oeis".
  88. ^ "A003368 - Oeis".
  89. ^ a b c d e f g h i j k l m "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 9 June 2016. Retrieved 12 June 2016.
  90. ^ "A002061 - Oeis".
  91. ^ "A003349 - Oeis".
  92. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A001105 (2*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  93. ^ "A003294 - Oeis".
  94. ^ Sloane, N. J. A. (ed.). "Sequence A007504 (Sum of the first n primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 February 2024.
  95. ^ Sloane, N. J. A. (ed.). "Sequence A127337 (Numbers that are the sum of 10 consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 February 2024.
  96. ^ Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  97. ^ a b c "A035137 - Oeis".
  98. ^ "A347565: Primes p such that A241014(A000720(p)) is +1 or -1". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 25 March 2022. Retrieved 19 January 2022.
  99. ^ "A003325 - Oeis".
  100. ^ "A195162 - Oeis".
  101. ^ "A006532 - Oeis".
  102. ^ "A341450 - Oeis".
  103. ^ a b c Sloane, N. J. A. (ed.). "Sequence A006128 (Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  104. ^ a b "A006567 - Oeis".
  105. ^ a b "A003354 - Oeis".
  106. ^ a b c d e f g h "Sloane's A000566 : Heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 11 June 2016. Retrieved 12 June 2016.
  107. ^ a b c d e f g "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 9 June 2016. Retrieved 12 June 2016.
  108. ^ "A273873 - Oeis".
  109. ^ "A292457 - Oeis".
  110. ^ "A073592 - Oeis".
  111. ^ a b c d e f g h i j "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 10 June 2016. Retrieved 12 June 2016.
  112. ^ a b c "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 10 June 2016. Retrieved 12 June 2016.
  113. ^ "A077043 - Oeis".
  114. ^ "A056107 - Oeis".
  115. ^ "A025147 - Oeis".
  116. ^ "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 9 June 2016. Retrieved 12 June 2016.
  117. ^ "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 4 March 2016. Retrieved 12 June 2016.
  118. ^ "A033996 - Oeis".
  119. ^ "A018900 - Oeis".
  120. ^ "A046308 - Oeis".
  121. ^ "Sloane's A001232 : Numbers n such that 9*n = (n written backwards)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 17 October 2015. Retrieved 14 June 2016.
  122. ^ "A003350 - Oeis".
  123. ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 163
  124. ^ a b c d e "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 11 June 2016. Retrieved 12 June 2016.
  125. ^ "A003355 - Oeis".
  126. ^ "A051682 - Oeis".
  127. ^ a b c Sloane, N. J. A. (ed.). "Sequence A323657 (Number of strict solid partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  128. ^ "A121029 - Oeis".
  129. ^ "A292449 - Oeis".
  130. ^ Sloane, N. J. A. (ed.). "Sequence A087188 (number of partitions of n into distinct squarefree parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  131. ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers: 2*n^2 + 6*n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  132. ^ a b c d e f g h i "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  133. ^ a b "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  134. ^ "Sloane's A002997 : Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  135. ^ a b c d e "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  136. ^ a b Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  137. ^ a b c Sloane, N. J. A. (ed.). "Sequence A051890 (2*(n^2 - n + 1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  138. ^ Sloane, N. J. A. (ed.). "Sequence A319560 (Number of non-isomorphic strict T_0 multiset partitions of weight n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  139. ^ a b c Sloane, N. J. A. (ed.). "Sequence A028916 (Friedlander-Iwaniec primes: Primes of form a^2 + b^4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  140. ^ Sloane, N. J. A. (ed.). "Sequence A057732 (Numbers k such that 2^k + 3 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  141. ^ a b Sloane, N. J. A. (ed.). "Sequence A046376 (Palindromes with exactly 2 palindromic prime factors (counted with multiplicity), and no other prime factors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  142. ^ Sloane, N. J. A. (ed.). "Sequence A128455 (Numbers k such that 9^k - 2 is a prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  143. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A000009 (Expansion of Product_{m > 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  144. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A318949 (Number of ways to write n as an orderless product of orderless sums)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  145. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A038499 (Number of partitions of n into a prime number of parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  146. ^ a b Sloane, N. J. A. (ed.). "Sequence A006748 (Number of diagonally symmetric polyominoes with n cells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  147. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A210000 (Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
  148. ^ Sloane, N. J. A. (ed.). "Sequence A033995 (Number of bipartite graphs with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  149. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  150. ^ a b c d e "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  151. ^ Sloane, N. J. A. (ed.). "Sequence A062801 (Number of 2 X 2 non-singular integer matrices with entries from {0,...,n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
  152. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A000096 (n*(n+3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  153. ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  154. ^ a b c Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  155. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  156. ^ Sloane, N. J. A. (ed.). "Sequence A005380". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  157. ^ Sloane, N. J. A. (ed.). "Sequence A051026 (Number of primitive subsequences of 1, 2, ..., n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  158. ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  159. ^ Sloane, N. J. A. (ed.). "Sequence A080040 (2*a(n-1) + 2*a(n-2) for n > 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  160. ^ Sloane, N. J. A. (ed.). "Sequence A264237 (Sum of values of vertices at level n of the hyperbolic Pascal pyramid)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  161. ^ a b Sloane, N. J. A. (ed.). "Sequence A033991 (n*(4*n-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  162. ^ "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  163. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  164. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A006315 (Numbers n such that n^32 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  165. ^ Sloane, N. J. A. (ed.). "Sequence A185982 (Triangle read by rows: number of set partitions of n elements with k connectors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  166. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A007534 (Even numbers that are not the sum of a pair of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  167. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A050993 (5-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  168. ^ Sloane, N. J. A. (ed.). "Sequence A006094 (Products of 2 successive primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  169. ^ Sloane, N. J. A. (ed.). "Sequence A046368 (Products of two palindromic primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  170. ^ "1150 (number)". The encyclopedia of numbers.
  171. ^ a b "Sloane's A000101 : Increasing gaps between primes (upper end)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 10 July 2016.
  172. ^ a b "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  173. ^ a b c d "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  174. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  175. ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  176. ^ a b c "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  177. ^ "Sloane's A069125 : a(n) = (11*n^2 - 11*n + 2)/2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  178. ^ "1157 (number)". The encyclopedia of numbers.
  179. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  180. ^ a b Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
  181. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  182. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  183. ^ Sloane, N. J. A. (ed.). "Sequence A055887 (Number of ordered partitions of partitions)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  184. ^ a b c Sloane, N. J. A. (ed.). "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  185. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A018805". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  186. ^ Sloane, N. J. A. (ed.). "Sequence A024816 (Antisigma(n): Sum of the numbers less than n that do not divide n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  187. ^ "A063776 - OEIS". oeis.org.
  188. ^ "A000256 - OEIS". oeis.org.
  189. ^ "1179 (number)". The encyclopedia of numbers.
  190. ^ "A000339 - OEIS". oeis.org.
  191. ^ "A271269 - OEIS". oeis.org.
  192. ^ "A000031 - OEIS". oeis.org.
  193. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
  194. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A051424 (Number of partitions of n into pairwise relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  195. ^ a b "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  196. ^ "A121038 - OEIS". oeis.org.
  197. ^ a b Sloane, N. J. A. (ed.). "Sequence A005449 (Second pentagonal numbers: n*(3*n + 1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  198. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  199. ^ "A175654 - OEIS". oeis.org.
  200. ^ oeis.org/A062092
  201. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A024916 (Sum_1^n sigma(k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  202. ^ a b c d e >Sloane, N. J. A. (ed.). "Sequence A080663 (3*n^2 - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  203. ^ Meehan, Eileen R., Why TV is not our fault: television programming, viewers, and who's really in control Lanham, MD: Rowman & Littlefield, 2005
  204. ^ "A265070 - OEIS". oeis.org.
  205. ^ "1204 (number)". The encyclopedia of numbers.
  206. ^ a b Sloane, N. J. A. (ed.). "Sequence A240574 (Number of partitions of n such that the number of odd parts is a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  207. ^ "A303815 - OEIS". oeis.org.
  208. ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A098237 (Composite de Polignac numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  209. ^ Sloane, N. J. A. (ed.). "Sequence A337070 (Number of strict chains of divisors starting with the superprimorial A006939(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  210. ^ Higgins, ibid.
  211. ^ Sloane, N. J. A. (ed.). "Sequence A000070 (Sum_{0..n} A000041(k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  212. ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  213. ^ a b c d e f "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  214. ^ a b Sloane, N. J. A. (ed.). "Sequence A006355 (Number of binary vectors of length n containing no singletons)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  215. ^ "Sloane's A001110 : Square triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  216. ^ a b c d e "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  217. ^ Sloane, N. J. A. (ed.). "Sequence A303815 (Generalized 29-gonal (or icosienneagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  218. ^ Sloane, N. J. A. (ed.). "Sequence A249911 (60-gonal (hexacontagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  219. ^ "A004111 - OEIS". oeis.org.
  220. ^ "A061262 - OEIS". oeis.org.
  221. ^ a b c Sloane, N. J. A. (ed.). "Sequence A008302 (Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product{0..n-1} (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). Also enumerates permutations by their major index)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  222. ^ "A006154 - OEIS". oeis.org.
  223. ^ "A000045 - OEIS". oeis.org.
  224. ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  225. ^ "A160160 - OEIS". oeis.org.
  226. ^ "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  227. ^ Sloane, N. J. A. (ed.). "Sequence A126796 (Number of complete partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  228. ^ oeis.org/A305843
  229. ^ "A007690 - OEIS". oeis.org.
  230. ^ "Sloane's A033819 : Trimorphic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  231. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A058331 (2*n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  232. ^ a b c Sloane, N. J. A. (ed.). "Sequence A144300 (Number of partitions of n minus number of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  233. ^ Sloane, N. J. A. (ed.). "Sequence A000837 (Number of partitions of n into relatively prime parts. Also aperiodic partitions.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  234. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  235. ^ a b Sloane, N. J. A. (ed.). "Sequence A193757 (Numbers which can be written with their digits in order and using only a plus and a squaring operator)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  236. ^ a b "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  237. ^ a b c d e "Sloane's A014575 : Vampire numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  238. ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  239. ^ a b Sloane, N. J. A. (ed.). "Sequence A070169 (Rounded total surface area of a regular tetrahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  240. ^ a b c Sloane, N. J. A. (ed.). "Sequence A003238 (Number of rooted trees with n vertices in which vertices at the same level have the same degree)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  241. ^ a b c Sloane, N. J. A. (ed.). "Sequence A023894 (Number of partitions of n into prime power parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  242. ^ a b c Sloane, N. J. A. (ed.). "Sequence A072895 (Least k for the Theodorus spiral to complete n revolutions)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  243. ^ Sloane, N. J. A. (ed.). "Sequence A100040 (2*n^2 + n - 5)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  244. ^ a b Sloane, N. J. A. (ed.). "Sequence A051349 (Sum of first n nonprimes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  245. ^ a b Sloane, N. J. A. (ed.). "Sequence A033286 (n * prime(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  246. ^ a b Sloane, N. J. A. (ed.). "Sequence A084849 (1 + n + 2*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  247. ^ a b Sloane, N. J. A. (ed.). "Sequence A000930 (Narayana's cows sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  248. ^ Sloane, N. J. A. (ed.). "Sequence A001792 ((n+2)*2^(n-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  249. ^ Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  250. ^ Sloane, N. J. A. (ed.). "Sequence A216492 (Number of inequivalent connected planar figures that can be formed from n 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  251. ^ Sloane, N. J. A. (ed.). "Sequence A007318 (Pascal's triangle read by rows)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  252. ^ Sloane, N. J. A. (ed.). "Sequence A014574 (Average of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  253. ^ Sloane, N. J. A. (ed.). "Sequence A173831 (Largest prime < n^4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  254. ^ Sloane, N. J. A. (ed.). "Sequence A006872 (Numbers k such that phi(k) equals phi(sigma(k)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  255. ^ Sloane, N. J. A. (ed.). "Sequence A014285 (Sum_{1..n} j*prime(j))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  256. ^ a b Sloane, N. J. A. (ed.). "Sequence A071400 (Rounded volume of a regular octahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  257. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A003114 (Number of partitions of n into parts 5k+1 or 5k+4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  258. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A033548 (Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  259. ^ Sloane, N. J. A. (ed.). "Sequence A000055 (Number of trees with n unlabeled nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  260. ^ "A124826 - OEIS". oeis.org.
  261. ^ "A142005 - OEIS". oeis.org.
  262. ^ a b Sloane, N. J. A. (ed.). "Sequence A338470 (Number of integer partitions of n with no part dividing all the others)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  263. ^ "A066186 - OEIS". oeis.org.
  264. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A304716 (Number of integer partitions of n whose distinct parts are connected)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  265. ^ "A115073 - OEIS". oeis.org.
  266. ^ "A061256 - OEIS". oeis.org.
  267. ^ "A061954 - OEIS". oeis.org.
  268. ^ Sloane, N. J. A. (ed.). "Sequence A057465 (Numbers k such that k^512 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  269. ^ "A030299 - OEIS". oeis.org.
  270. ^ a b "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  271. ^ a b Sloane, N. J. A. (ed.). "Sequence A005894 (Centered tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  272. ^ Sloane, N. J. A. (ed.). "Sequence A018806 (Sum of gcd(x, y))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  273. ^ Sloane, N. J. A. (ed.). "Sequence A018227 (Magic numbers: atoms with full shells containing any of these numbers of electrons are considered electronically stable)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  274. ^ "A005064 - OEIS". oeis.org.
  275. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  276. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  277. ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A090781 (Numbers that can be expressed as the difference of the squares of primes in just one distinct way)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  278. ^ a b Sloane, N. J. A. (ed.). "Sequence A056809 (Numbers k such that k, k+1 and k+2 are products of two primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  279. ^ "A316473 - OEIS". oeis.org.
  280. ^ "A000032 - OEIS". oeis.org.
  281. ^ "1348 (number)". The encyclopedia of numbers.
  282. ^ a b Sloane, N. J. A. (ed.). "Sequence A101624 (Stern-Jacobsthal number)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  283. ^ Sloane, N. J. A. (ed.). "Sequence A064228 (From Recamán's sequence (A005132): values of n achieving records in A057167)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  284. ^ Sloane, N. J. A. (ed.). "Sequence A057167 (Term in Recamán's sequence A005132 where n appears for first time, or -1 if n never appears)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  285. ^ Sloane, N. J. A. (ed.). "Sequence A064227 (From Recamán's sequence (A005132): record values in A057167)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  286. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000603". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  287. ^ Sloane, N. J. A. (ed.). "Sequence A000960 (Flavius Josephus's sieve: Start with the natural numbers; at the k-th sieving step, remove every (k+1)-st term of the sequence remaining after the (k-1)-st sieving step; iterate)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  288. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A330224 (Number of achiral integer partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  289. ^ Sloane, N. J. A. (ed.). "Sequence A001610 (a(n-1) + a(n-2) + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  290. ^ Sloane, N. J. A. (ed.). "Sequence A000032 (Lucas numbers: L(n-1) + L(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  291. ^ a b "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  292. ^ Sloane, N. J. A. (ed.). "Sequence A005578 (Arima sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  293. ^ a b c Sloane, N. J. A. (ed.). "Sequence A001157 (sigma_2(n): sum of squares of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  294. ^ a b Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  295. ^ a b c Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  296. ^ a b Sloane, N. J. A. (ed.). "Sequence A005945 (Number of n-step mappings with 4 inputs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  297. ^ "A001631 - OEIS". oeis.org. Retrieved 25 June 2023.
  298. ^ Sloane, N. J. A. (ed.). "Sequence A088274 (Numbers k such that 10^k + 7 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  299. ^ Sloane, N. J. A. (ed.). "Sequence A000111 (Euler or up/down numbers: e.g.f. sec(x) + tan(x))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  300. ^ Sloane, N. J. A. (ed.). "Sequence A002414 (Octagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  301. ^ "Sloane's A001567 : Fermat pseudoprimes to base 2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  302. ^ "Sloane's A050217 : Super-Poulet numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  303. ^ Sloane, N. J. A. (ed.). "Sequence A054552 (4*n^2 - 3*n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  304. ^ Sloane, N. J. A. (ed.). "Sequence A017919 (Powers of sqrt(5) rounded down)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  305. ^ Sloane, N. J. A. (ed.). "Sequence A109308 (Lesser emirps (primes whose digit reversal is a larger prime))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  306. ^ a b Sloane, N. J. A. (ed.). "Sequence A007865 (Number of sum-free subsets of {1, ..., n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
  307. ^ a b Sloane, N. J. A. (ed.). "Sequence A325349 (Number of integer partitions of n whose augmented differences are distinct)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  308. ^ a b Sloane, N. J. A. (ed.). "Sequence A051400 (Smallest value of x such that M(x) equals n, where M() is Mertens's function A002321)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  309. ^ "Sloane's A000682 : Semimeanders". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  310. ^ Sloane, N. J. A. (ed.). "Sequence A002445 (Denominators of Bernoulli numbers B_{2n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
  311. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A045918 (Describe n. Also called the "Say What You See" or "Look and Say" sequence LS(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  312. ^ a b Sloane, N. J. A. (ed.). "Sequence A050710 (Smallest composite that when added to sum of prime factors reaches a prime after n iterations)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  313. ^ a b Sloane, N. J. A. (ed.). "Sequence A067538 (Number of partitions of n in which the number of parts divides n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  314. ^ a b "Sloane's A051015 : Zeisel numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  315. ^ a b c Sloane, N. J. A. (ed.). "Sequence A059845 (n*(3*n + 11)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  316. ^ Sloane, N. J. A. (ed.). "Sequence A000097 (Number of partitions of n if there are two kinds of 1's and two kinds of 2's)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  317. ^ a b Sloane, N. J. A. (ed.). "Sequence A061068 (Primes which are the sum of a prime and its subscript)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  318. ^ Sloane, N. J. A. (ed.). "Sequence A001359 (Lesser of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  319. ^ Sloane, N. J. A. (ed.). "Sequence A001764 (binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  320. ^ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  321. ^ a b Sloane, N. J. A. (ed.). "Sequence A071399 (Rounded volume of a regular tetrahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  322. ^ a b c Sloane, N. J. A. (ed.). "Sequence A006832 (Discriminants of totally real cubic fields)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  323. ^ a b Sloane, N. J. A. (ed.). "Sequence A003037 (Smallest number of complexity n: smallest number requiring n 1's to build using +, * and ^)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  324. ^ Sloane, N. J. A. (ed.). "Sequence A005259 (Apery (Apéry) numbers: Sum_0^n (binomial(n,k)*binomial(n+k,k))^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  325. ^ a b Sloane, N. J. A. (ed.). "Sequence A062325 (Numbers k for which phi(prime(k)) is a square)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  326. ^ a b Sloane, N. J. A. (ed.). "Sequence A011379 (n^2*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  327. ^ a b Sloane, N. J. A. (ed.). "Sequence A005918 (Number of points on surface of square pyramid: 3*n^2 + 2 (n>0))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  328. ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A011257 (Geometric mean of phi(n) and sigma(n) is an integer)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  329. ^ Sloane, N. J. A. (ed.). "Sequence A007678 (Number of regions in regular n-gon with all diagonals drawn)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  330. ^ a b Sloane, N. J. A. (ed.). "Sequence A056220 (2*n^2 - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  331. ^ Sloane, N. J. A. (ed.). "Sequence A028569 (n*(n + 9))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  332. ^ Sloane, N. J. A. (ed.). "Sequence A071398 (Rounded total surface area of a regular icosahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  333. ^ Sloane, N. J. A. (ed.). "Sequence A085831 (Sum_1^{2^n} d(k) where d(k) is the number of divisors of k (A000005))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  334. ^ Sloane, N. J. A. (ed.). "Sequence A064410 (Number of partitions of n with zero crank)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  335. ^ Sloane, N. J. A. (ed.). "Sequence A075207 (Number of polyhexes with n cells that tile the plane by translation)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  336. ^ a b "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  337. ^ Sloane, N. J. A. (ed.). "Sequence A015128 (Number of overpartitions of n: an overpartition of n is an ordered sequence of nonincreasing integers that sum to n, where the first occurrence of each integer may be overlined)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  338. ^ Sloane, N. J. A. (ed.). "Sequence A006578 (Triangular numbers plus quarter squares: n*(n+1)/2 + floor(n^2/4) (i.e., A000217(n) + A002620(n)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  339. ^ a b Sloane, N. J. A. (ed.). "Sequence A098859 (Number of partitions of n into parts each of which is used a different number of times)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  340. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A307958 (Coreful perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  341. ^ Sloane, N. J. A. (ed.). "Sequence A097979 (Total number of largest parts in all compositions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  342. ^ Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  343. ^ Sloane, N. J. A. (ed.). "Sequence A006330 (Number of corners, or planar partitions of n with only one row and one column)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  344. ^ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  345. ^ Sloane, N. J. A. (ed.). "Sequence A114411 (Triple primorial n###)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  346. ^ a b Sloane, N. J. A. (ed.). "Sequence A034296 (Number of flat partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  347. ^ a b Sloane, N. J. A. (ed.). "Sequence A084647 (Hypotenuses for which there exist exactly 3 distinct integer triangles)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  348. ^ a b Sloane, N. J. A. (ed.). "Sequence A002071 (Number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most the n-th prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  349. ^ Sloane, N. J. A. (ed.). "Sequence A325325 (Number of integer partitions of n with distinct differences between successive parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  350. ^ Sloane, N. J. A. (ed.). "Sequence A325858 (Number of Golomb partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  351. ^ Sloane, N. J. A. (ed.). "Sequence A018000 (Powers of cube root of 9 rounded down)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  352. ^ Sloane, N. J. A. (ed.). "Sequence A062198 (Sum of first n semiprimes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  353. ^ Sloane, N. J. A. (ed.). "Sequence A038147 (Number of polyhexes with n cells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  354. ^ a b Sloane, N. J. A. (ed.). "Sequence A000702 (number of conjugacy classes in the alternating group A_n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  355. ^ Sloane, N. J. A. (ed.). "Sequence A001970 (Functional determinants; partitions of partitions; Euler transform applied twice to all 1's sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  356. ^ Sloane, N. J. A. (ed.). "Sequence A071396 (Rounded total surface area of a regular octahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  357. ^ Sloane, N. J. A. (ed.). "Sequence A000084 (Number of series-parallel networks with n unlabeled edges. Also called yoke-chains by Cayley and MacMahon)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  358. ^ Sloane, N. J. A. (ed.). "Sequence A000615 (Threshold functions of exactly n variables)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  359. ^ Sloane, N. J. A. (ed.). "Sequence A100129 (Numbers k such that 2^k starts with k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  360. ^ Sloane, N. J. A. (ed.). "Sequence A000057 (Primes dividing all Fibonacci sequences)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  361. ^ Sloane, N. J. A. (ed.). "Sequence A319066 (Number of partitions of integer partitions of n where all parts have the same length)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  362. ^ Sloane, N. J. A. (ed.). "Sequence A056327 (Number of reversible string structures with n beads using exactly three different colors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  363. ^ Sloane, N. J. A. (ed.). "Sequence A002720 (Number of partial permutations of an n-set; number of n X n binary matrices with at most one 1 in each row and column)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  364. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A065381 (Primes not of the form p + 2^k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  365. ^ Sloane, N. J. A. (ed.). "Sequence A140090 (n*(3*n + 7)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  366. ^ Sloane, N. J. A. (ed.). "Sequence A169942 (Number of Golomb rulers of length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  367. ^ Sloane, N. J. A. (ed.). "Sequence A169952 (Second entry in row n of triangle in A169950)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  368. ^ Sloane, N. J. A. (ed.). "Sequence A034962 (Primes that are the sum of three consecutive primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  369. ^ Sloane, N. J. A. (ed.). "Sequence A046386 (Products of four distinct primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  370. ^ Sloane, N. J. A. (ed.). "Sequence A127106 (Numbers n such that n^2 divides 6^n-1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  371. ^ a b Sloane, N. J. A. (ed.). "Sequence A008406 (Triangle T(n,k) read by rows, giving number of graphs with n nodes and k edges))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  372. ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  373. ^ Sloane, N. J. A. (ed.). "Sequence A057660 (Sum_{1..n} n/gcd(n,k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  374. ^ Sloane, N. J. A. (ed.). "Sequence A088319 (Ordered hypotenuses of primitive Pythagorean triangles having legs that add up to a square)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  375. ^ a b Sloane, N. J. A. (ed.). "Sequence A052486 (Achilles numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  376. ^ Sloane, N. J. A. (ed.). "Sequence A056995 (Numbers k such that k^256 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  377. ^ "Sloane's A005231 : Odd abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  378. ^ Sloane, N. J. A. (ed.). "Sequence A056026 (Numbers k such that k^14 is congruent with 1 (mod 15^2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  379. ^ Sloane, N. J. A. (ed.). "Sequence A076409 (Sum of the quadratic residues of prime(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  380. ^ Sloane, N. J. A. (ed.). "Sequence A070142 (Numbers n such that [A070080(n), A070081(n), A070082(n)] is an integer triangle with integer area)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  381. ^ Sloane, N. J. A. (ed.). "Sequence A033428 (3*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  382. ^ Sloane, N. J. A. (ed.). "Sequence A071402 (Rounded volume of a regular icosahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  383. ^ Sloane, N. J. A. (ed.). "Sequence A326123 (a(n) is the sum of all divisors of the first n odd numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  384. ^ Sloane, N. J. A. (ed.). "Sequence A006327 (Fibonacci(n) - 3. Number of total preorders)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  385. ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  386. ^ Sloane, N. J. A. (ed.). "Sequence A100145 (Structured great rhombicosidodecahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  387. ^ a b Sloane, N. J. A. (ed.). "Sequence A064174 (Number of partitions of n with nonnegative rank)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  388. ^ Sloane, N. J. A. (ed.). "Sequence A023360 (Number of compositions of n into prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  389. ^ Sloane, N. J. A. (ed.). "Sequence A103473 (Number of polyominoes consisting of 7 regular unit n-gons)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  390. ^ Sloane, N. J. A. (ed.). "Sequence A007584 (9-gonal (or enneagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  391. ^ Sloane, N. J. A. (ed.). "Sequence A022004 (Initial members of prime triples (p, p+2, p+6))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  392. ^ Sloane, N. J. A. (ed.). "Sequence A006489 (Numbers k such that k-6, k, and k+6 are primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  393. ^ Sloane, N. J. A. (ed.). "Sequence A213427 (Number of ways of refining the partition n^1 to get 1^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  394. ^ Sloane, N. J. A. (ed.). "Sequence A134602 (Composite numbers such that the square mean of their prime factors is a nonprime integer (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  395. ^ Sloane, N. J. A. (ed.). "Sequence A084990 (n*(n^2+3*n-1)/3)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  396. ^ Sloane, N. J. A. (ed.). "Sequence A077068 (Semiprimes of the form prime + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  397. ^ Sloane, N. J. A. (ed.). "Sequence A115160 (Numbers that are not the sum of two triangular numbers and a fourth power)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  398. ^ a b Sloane, N. J. A. (ed.). "Sequence A046092 (4 times triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  399. ^ Sloane, N. J. A. (ed.). "Sequence A005382 (Primes p such that 2p-1 is also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  400. ^ Sloane, N. J. A. (ed.). "Sequence A001339 (Sum_{0..n} (k+1)! binomial(n,k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  401. ^ Sloane, N. J. A. (ed.). "Sequence A007290 (2*binomial(n,3))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  402. ^ Sloane, N. J. A. (ed.). "Sequence A058360 (Number of partitions of n whose reciprocal sum is an integer)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  403. ^ Sloane, N. J. A. (ed.). "Sequence A046931 (Prime islands: least prime whose adjacent primes are exactly 2n apart)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  404. ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  405. ^ Sloane, N. J. A. (ed.). "Sequence A056613 (Number of n-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  406. ^ Sloane, N. J. A. (ed.). "Sequence A068140 (Smaller of two consecutive numbers each divisible by a cube greater than one)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  407. ^ Sloane, N. J. A. (ed.). "Sequence A030272 (Number of partitions of n^3 into distinct cubes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  408. ^ Sloane, N. J. A. (ed.). "Sequence A018818 (Number of partitions of n into divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  409. ^ Sloane, N. J. A. (ed.). "Sequence A071401 (Rounded volume of a regular dodecahedron with edge length n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  410. ^ a b c "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  411. ^ Sloane, N. J. A. (ed.). "Sequence A059802 (Numbers k such that 5^k - 4^k is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  412. ^ a b Sloane, N. J. A. (ed.). "Sequence A082982 (Numbers k such that k, k+1 and k+2 are sums of 2 squares)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  413. ^ Sloane, N. J. A. (ed.). "Sequence A057562 (Number of partitions of n into parts all relatively prime to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  414. ^ Sloane, N. J. A. (ed.). "Sequence A000230 (smallest prime p such that there is a gap of exactly 2n between p and next prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  415. ^ Sloane, N. J. A. (ed.). "Sequence A261983 (Number of compositions of n such that at least two adjacent parts are equal)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  416. ^ Sloane, N. J. A. (ed.). "Sequence A053781 (Numbers k that divide the sum of the first k composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  417. ^ Sloane, N. J. A. (ed.). "Sequence A140480 (RMS numbers: numbers n such that root mean square of divisors of n is an integer)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  418. ^ Sloane, N. J. A. (ed.). "Sequence A023108 (Positive integers which apparently never result in a palindrome under repeated applications of the function A056964(x))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  419. ^ Sloane, N. J. A. (ed.). "Sequence A286518 (Number of finite connected sets of positive integers greater than one with least common multiple n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  420. ^ Sloane, N. J. A. (ed.). "Sequence A004041 (Scaled sums of odd reciprocals: (2*n + 1)!!*(Sum_{0..n} 1/(2*k + 1)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  421. ^ Sloane, N. J. A. (ed.). "Sequence A023359 (Number of compositions (ordered partitions) of n into powers of 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  422. ^ Sloane, N. J. A. (ed.). "Sequence A000787 (Strobogrammatic numbers: the same upside down)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  423. ^ Sloane, N. J. A. (ed.). "Sequence A224930 (Numbers n such that n divides the concatenation of all divisors in descending order)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  424. ^ Sloane, N. J. A. (ed.). "Sequence A294286 (Sum of the squares of the parts in the partitions of n into two distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  425. ^ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  426. ^ Sloane, N. J. A. (ed.). "Sequence A020989 ((5*4^n - 2)/3)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  427. ^ Sloane, N. J. A. (ed.). "Sequence A331378 (Numbers whose product of prime indices is divisible by their sum of prime factors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  428. ^ Sloane, N. J. A. (ed.). "Sequence A301700 (Number of aperiodic rooted trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  429. ^ Sloane, N. J. A. (ed.). "Sequence A331452 (number of regions (or cells) formed by drawing the line segments connecting any two of the 2*(m+n) perimeter points of an m X n grid of squares)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  430. ^ Sloane, N. J. A. (ed.). "Sequence A056045 ("Sum_{d divides n}(binomial(n,d))")". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  431. ^ "Sloane's A007850 : Giuga numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  432. ^ Sloane, N. J. A. (ed.). "Sequence A161757 ((prime(n))^2 - (nonprime(n))^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  433. ^ Sloane, N. J. A. (ed.). "Sequence A078374 (Number of partitions of n into distinct and relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  434. ^ Sloane, N. J. A. (ed.). "Sequence A167008 (Sum_{0..n} C(n,k)^k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  435. ^ Sloane, N. J. A. (ed.). "Sequence A033581 (6*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  436. ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  437. ^ Sloane, N. J. A. (ed.). "Sequence A350507 (Number of (not necessarily connected) unit-distance graphs on n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  438. ^ Sloane, N. J. A. (ed.). "Sequence A102627 (Number of partitions of n into distinct parts in which the number of parts divides n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  439. ^ Sloane, N. J. A. (ed.). "Sequence A216955 (number of binary sequences of length n and curling number k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  440. ^ Sloane, N. J. A. (ed.). "Sequence A001523 (Number of stacks, or planar partitions of n; also weakly unimodal compositions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  441. ^ Sloane, N. J. A. (ed.). "Sequence A065764 (Sum of divisors of square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  442. ^ Sloane, N. J. A. (ed.). "Sequence A220881 (Number of nonequivalent dissections of an n-gon into n-3 polygons by nonintersecting diagonals up to rotation)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  443. ^ Sloane, N. J. A. (ed.). "Sequence A154964 (3*a(n-1) + 6*a(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  444. ^ Sloane, N. J. A. (ed.). "Sequence A055327 (Triangle of rooted identity trees with n nodes and k leaves)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  445. ^ Sloane, N. J. A. (ed.). "Sequence A316322 (Sum of piles of first n primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  446. ^ Sloane, N. J. A. (ed.). "Sequence A045944 (Rhombic matchstick numbers: n*(3*n+2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  447. ^ Sloane, N. J. A. (ed.). "Sequence A127816 (least k such that the remainder when 6^k is divided by k is n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  448. ^ Sloane, N. J. A. (ed.). "Sequence A005317 ((2^n + C(2*n,n))/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  449. ^ Sloane, N. J. A. (ed.). "Sequence A064118 (Numbers k such that the first k digits of e form a prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  450. ^ Sloane, N. J. A. (ed.). "Sequence A325860 (Number of subsets of {1..n} such that every pair of distinct elements has a different quotient)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  451. ^ Sloane, N. J. A. (ed.). "Sequence A073592 (Euler transform of negative integers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  452. ^ Sloane, N. J. A. (ed.). "Sequence A025047 (Alternating compositions, i.e., compositions with alternating increases and decreases, starting with either an increase or a decrease)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  453. ^ Sloane, N. J. A. (ed.). "Sequence A288253 (Number of heptagons that can be formed with perimeter n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  454. ^ Sloane, N. J. A. (ed.). "Sequence A235488 (Squarefree numbers which yield zero when their prime factors are xored together)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  455. ^ Sloane, N. J. A. (ed.). "Sequence A075213 (Number of polyhexes with n cells that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  456. ^ "Sloane's A054377 : Primary pseudoperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  457. ^ Kellner, Bernard C.; 'The equation denom(Bn) = n has only one solution'
  458. ^ Sloane, N. J. A. (ed.). "Sequence A006318 (Large Schröder numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 May 2016.
  459. ^ "Sloane's A000058 : Sylvester's sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  460. ^ Sloane, N. J. A. (ed.). "Sequence A083186 (Sum of first n primes whose indices are primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  461. ^ Sloane, N. J. A. (ed.). "Sequence A005260 (Sum_{0..n} binomial(n,k)^4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  462. ^ Sloane, N. J. A. (ed.). "Sequence A056877 (Number of polyominoes with n cells, symmetric about two orthogonal axes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  463. ^ Sloane, N. J. A. (ed.). "Sequence A061801 ((7*6^n - 2)/5)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  464. ^ Sloane, N. J. A. (ed.). "Sequence A152927 (Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 4-gonal polygonal components chained with string components of length 1 as k varies)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  465. ^ Sloane, N. J. A. (ed.). "Sequence A037032 (Total number of prime parts in all partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  466. ^ Sloane, N. J. A. (ed.). "Sequence A101301 (The sum of the first n primes, minus n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  467. ^ Sloane, N. J. A. (ed.). "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2 June 2022.
  468. ^ Sloane, N. J. A. (ed.). "Sequence A000230 (smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  469. ^ Sloane, N. J. A. (ed.). "Sequence A004068 (Number of atoms in a decahedron with n shells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  470. ^ Sloane, N. J. A. (ed.). "Sequence A001905 (From higher-order Bernoulli numbers: absolute value of numerator of D-number D2n(2n-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  471. ^ Sloane, N. J. A. (ed.). "Sequence A214083 (floor(n!^(1/3)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  472. ^ Sloane, N. J. A. (ed.). "Sequence A001208 (solution to the postage stamp problem with 3 denominations and n stamps)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  473. ^ Sloane, N. J. A. (ed.). "Sequence A000081 (Number of unlabeled rooted trees with n nodes (or connected functions with a fixed point))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  474. ^ Sloane, N. J. A. (ed.). "Sequence A039771 (Numbers k such that phi(k) is a perfect cube)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  475. ^ Sloane, N. J. A. (ed.). "Sequence A024026 (3^n - n^3)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  476. ^ Sloane, N. J. A. (ed.). "Sequence A235945 (Number of partitions of n containing at least one prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  477. ^ Sloane, N. J. A. (ed.). "Sequence A354493 (Number of quantales on n elements, up to isomorphism)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  478. ^ Sloane, N. J. A. (ed.). "Sequence A088144 (Sum of primitive roots of n-th prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  479. ^ Sloane, N. J. A. (ed.). "Sequence A000166 (Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  480. ^ Sloane, N. J. A. (ed.). "Sequence A000240 (Rencontres numbers: number of permutations of [n] with exactly one fixed point)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  481. ^ Sloane, N. J. A. (ed.). "Sequence A000602 (Number of n-node unrooted quartic trees; number of n-carbon alkanes C(n)H(2n+2) ignoring stereoisomers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  482. ^ ""Aztec Diamond"". Retrieved 20 September 2022.
  483. ^ Sloane, N. J. A. (ed.). "Sequence A082671 (Numbers n such that (n!-2)/2 is a prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  484. ^ Sloane, N. J. A. (ed.). "Sequence A023811 (Largest metadrome (number with digits in strict ascending order) in base n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  485. ^ Sloane, N. J. A. (ed.). "Sequence A000990 (Number of plane partitions of n with at most two rows)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  486. ^ Sloane, N. J. A. (ed.). "Sequence A164652 (Hultman numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  487. ^ Sloane, N. J. A. (ed.). "Sequence A007530 (Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  488. ^ Sloane, N. J. A. (ed.). "Sequence A057568 (Number of partitions of n where n divides the product of the parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  489. ^ Sloane, N. J. A. (ed.). "Sequence A011757 (prime(n^2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  490. ^ Sloane, N. J. A. (ed.). "Sequence A004799 (Self convolution of Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  491. ^ Sloane, N. J. A. (ed.). "Sequence A005920 (Tricapped prism numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  492. ^ Sloane, N. J. A. (ed.). "Sequence A000609 (Number of threshold functions of n or fewer variables)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  493. ^ Sloane, N. J. A. (ed.). "Sequence A259793 (Number of partitions of n^4 into fourth powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  494. ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  495. ^ Sloane, N. J. A. (ed.). "Sequence A002998 (Smallest multiple of n whose digits sum to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  496. ^ Sloane, N. J. A. (ed.). "Sequence A005987 (Number of symmetric plane partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  497. ^ Sloane, N. J. A. (ed.). "Sequence A023431 (Generalized Catalan Numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  498. ^ Sloane, N. J. A. (ed.). "Sequence A217135 (Numbers n such that 3^n - 8 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  499. ^ "Sloane's A034897 : Hyperperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  500. ^ Sloane, N. J. A. (ed.). "Sequence A240736 (Number of compositions of n having exactly one fixed point)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  501. ^ Sloane, N. J. A. (ed.). "Sequence A007070 (4*a(n-1) - 2*a(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  502. ^ Sloane, N. J. A. (ed.). "Sequence A000412 (Number of bipartite partitions of n white objects and 3 black ones)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  503. ^ Sloane, N. J. A. (ed.). "Sequence A027851 (Number of nonisomorphic semigroups of order n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  504. ^ Sloane, N. J. A. (ed.). "Sequence A003060 (Smallest number with reciprocal of period length n in decimal (base 10))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  505. ^ Sloane, N. J. A. (ed.). "Sequence A008514 (4-dimensional centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  506. ^ Sloane, N. J. A. (ed.). "Sequence A024012 (2^n - n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  507. ^ Sloane, N. J. A. (ed.). "Sequence A002845 (Number of distinct values taken by 2^2^...^2 (with n 2's and parentheses inserted in all possible ways))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  508. ^ "Sloane's A051870 : 18-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 June 2016.
  509. ^ Sloane, N. J. A. (ed.). "Sequence A045648 (Number of chiral n-ominoes in (n-1)-space, one cell labeled)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  510. ^ Sloane, N. J. A. (ed.). "Sequence A000127 (Maximal number of regions obtained by joining n points around a circle by straight lines. Also number of regions in 4-space formed by n-1 hyperplanes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  511. ^ Sloane, N. J. A. (ed.). "Sequence A178084 (Numbers k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  512. ^ a b Sloane, N. J. A. (ed.). "Sequence A007419 (Largest number not the sum of distinct n-th-order polygonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  513. ^ Sloane, N. J. A. (ed.). "Sequence A100953 (Number of partitions of n into relatively prime parts such that multiplicities of parts are also relatively prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  514. ^ Sloane, N. J. A. (ed.). "Sequence A226366 (Numbers k such that 5*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  515. ^ Sloane, N. J. A. (ed.). "Sequence A319014 (1*2*3 + 4*5*6 + 7*8*9 + 10*11*12 + 13*14*15 + 16*17*18 + ... + (up to n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  516. ^ Sloane, N. J. A. (ed.). "Sequence A055621 (Number of covers of an unlabeled n-set)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  517. ^ Sloane, N. J. A. (ed.). "Sequence A000522 (Total number of ordered k-tuples of distinct elements from an n-element set)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  518. ^ Sloane, N. J. A. (ed.). "Sequence A104621 (Heptanacci-Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  519. ^ Sloane, N. J. A. (ed.). "Sequence A005449 (Second pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  520. ^ Sloane, N. J. A. (ed.). "Sequence A002982 (Numbers n such that n! - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  521. ^ Sloane, N. J. A. (ed.). "Sequence A030238 (Backwards shallow diagonal sums of Catalan triangle A009766)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  522. ^ Sloane, N. J. A. (ed.). "Sequence A089046 (Least edge-length of a square dissectable into at least n squares in the Mrs. Perkins's quilt problem)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  523. ^ Sloane, N. J. A. (ed.). "Sequence A065900 (Numbers n such that sigma(n) equals sigma(n-1) + sigma(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  524. ^ Jon Froemke & Jerrold W. Grossman (February 1993). "A Mod-n Ackermann Function, or What's So Special About 1969?". The American Mathematical Monthly. Mathematical Association of America. 100 (2): 180–183. doi:10.2307/2323780. JSTOR 2323780.
  525. ^ Sloane, N. J. A. (ed.). "Sequence A052542 (2*a(n-1) + a(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  526. ^ Sloane, N. J. A. (ed.). "Sequence A024069 (6^n - n^7)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  527. ^ Sloane, N. J. A. (ed.). "Sequence A217076 (Numbers n such that (n^37-1)/(n-1) is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  528. ^ Sloane, N. J. A. (ed.). "Sequence A302545 (Number of non-isomorphic multiset partitions of weight n with no singletons)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  529. ^ Sloane, N. J. A. (ed.). "Sequence A277288 (Positive integers n such that n divides (3^n + 5))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  530. ^ Sloane, N. J. A. (ed.). "Sequence A187220 (Gullwing sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  531. ^ Sloane, N. J. A. (ed.). "Sequence A046351 (Palindromic composite numbers with only palindromic prime factors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  532. ^ Sloane, N. J. A. (ed.). "Sequence A000612 (Number of P-equivalence classes of switching functions of n or fewer variables, divided by 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  533. ^ OEISA059801
  534. ^ Sloane, N. J. A. (ed.). "Sequence A002470 (Glaisher's function W(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  535. ^ Sloane, N. J. A. (ed.). "Sequence A263341 (Triangle read by rows: T(n,k) is the number of unlabeled graphs on n vertices with independence number k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  536. ^ Sloane, N. J. A. (ed.). "Sequence A089085 (Numbers k such that (k! + 3)/3 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  537. ^ Sloane, N. J. A. (ed.). "Sequence A011755 (Sum_{1..n} k*phi(k))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  538. ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.,
  539. ^ Sloane, N. J. A. (ed.). "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  540. ^ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.