# 1000 (number)

(Redirected from 1627 (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
Unicode symbol(s)
Greek prefixchilia
Latin prefixmilli
Binary11111010002
Ternary11010013
Octal17508
Duodecimal6B412
Tamil
Chinese
Punjabi੧੦੦੦

It may also be described as the short thousand in historical discussion of medieval contexts where it might be confused with the Germanic concept of the "long thousand" (1200).

A period of 1,000 years is sometimes termed, after the Greek root, a chiliad. A chiliad of other objects means 1,000 of them.[1]

## Notation

• The decimal representation for one thousand is
• The SI prefix for a thousand units is "kilo-", abbreviated to "k"—for instance, a kilometre or "km" is a thousand metres.
• 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": 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 of America this is sometimes abbreviated with a "G" suffix.
• The factors of 1000 are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.[2]

## Properties

• 1000 is a Harshad number in base 10.
• The sum of Euler's totient function over the first 57 integers is 1000.
• Prime Curios! mentions that 1000 is the smallest number that generates three primes in the fastest way possible by concatenation of decremented numbers (1 000 999, 1 000 999 998 997, and 1 000 999 998 997 996 995 994 993 are prime). The criterion excludes counting the number itself.[3]

## Selected numbers in the range 1001–1999

### 1001 to 1099

1001 = sphenic number (7 × 11 × 13), pentagonal number, pentatope 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[4]
1005 = Mertens function zero, decagonal pyramidal number[5]
1006 = number that is the sum of 7 positive 5th powers[6]
1007 = number that is the sum of 8 positive 5th powers[7]
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.
1010 = 103 + 10,[8] Mertens function zero
1011 = the largest n such that 2n contains 101 and doesn't 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[9]
1012 = ternary number, (3210) quadruple triangular number (triangular number is 253),[10] number of partitions of 1 into reciprocals of positive integers <= 17 Egyptian fraction[9]
1013 = Sophie Germain prime,[11] centered square number,[12] Mertens function zero
1014 = 210-10,[13] Mertens function zero, sum of the nontriangular numbers between successive triangular numbers
1015 = square pyramidal number[14]
1016 = member of the Mian–Chowla sequence,[15] stella octangula number, number of cubes of edge length 1 required to make a hollow cube of edge length 14
1017 = generalized triacontagonal number[16]
1018 = Mertens function zero, 101816 + 1 is prime[17]
1019 = Sophie Germain prime,[11] safe prime[18]
1020 = polydivisible number
1021 = twin prime with 1019. It is also a Lucky prime.
1022 = Friedman number
1023 = the highest number one can count to on one's fingers using binary; number of compositions of 12 whose run-lengths are either weakly increasing or weakly decreasing;[19] also the 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.[20]
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 largest proven base-10 repunit prime,[21] Sophie Germain prime,[11] super-prime
1032 = sum of two distinct powers of 2 (1024 + 8)
1033 = emirp, twin prime with 1031
1034 = sum of 12 positive 9th powers[22]
1035 = triangular number,[23] hexagonal number[24]
1036 = central polygonal number[25]
1037 = number in E-toothpick sequence[26]
1038 = even integer that is an unordered sum of two primes in exactly n ways[27]
1039 = prime of the form 8n+7,[28] number of partitions of 30 that do not contain 1 as a part[29]
1040 = sum of distinct powers of 4[30]
1041 = sum of 11 positive 5th powers[31]
1042 = sum of 12 positive 5th powers[32]
1043 = number whose sum of even digits and sum of odd digits are even[33]
1044 = sum of distinct powers of 4[30]
1045 = octagonal number[34]
1046 = coefficient of f(q) (3rd order mock theta function)[35]
1047 = number of ways to split a strict composition of n into contiguous subsequences that have the same sum[36]
1048 = number of partitions of n into squarefree parts[37]
1049 = Sophie Germain prime,[11] highly cototient number[38]
1050 = 10508 to decimal becomes a pronic number (55210),[39] number of parts in all partitions of 29 into distinct parts[40]
1051 = centered pentagonal number,[41] centered decagonal number
1052 = number that is the sum of 9 positive 6th powers[42]
1053 = triangular matchstick number[43]
1054 = centered triangular number[44]
1055 = number that is the sum of 12 positive 6th powers[45]
1056 = pronic number[46]
1057 = central polygonal number[47]
1058 = number that is the sum of 4 positive 5th powers,[48] area of a square with diagonal 46[49]
1059 = number n such that n4 is written in the form of a sum of four positive 4th powers[50]
1060 = sum of the first 25 primes
1061 = emirp, twin prime with 1063
1062 = number that is not the sum of two palindromes[51]
1063 = super-prime, sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167); near-wall-sun-sun prime[52]
1064 = sum of two positive cubes[53]
1065 = generalized duodecagonal[54]
1066 = number whose sum of their divisors is a square[55]
1067 = number of strict integer partitions of n in which are empty or have smallest part not dividing the other ones[56]
1068 = number that is the sum of 7 positive 5th powers,[6] total number of parts in all partitions of 15[57]
1069 = emirp[58]
1070 = number that is the sum of 9 positive 5th powers[59]
1071 = heptagonal number[60]
1072 = centered heptagonal number[61]
1073 = number that is the sum of 12 positive 5th powers[32]
1074 = number that is not the sum of two palindromes[51]
1075 = number non-sum of two palindromes[51]
1076 = number of strict trees weight n[62]
1077 = number where 7 outnumbers every other digit in the number[63]
1078 = Euler transform of negative integers[64]
1079 = every positive integer is the sum of at most 1079 tenth powers.
1080 = pentagonal number[65]
1081 = triangular number,[23] member of Padovan sequence[66]
1082 = central polygonal number[25]
1083 = three-quarter square,[67] number of partitions of 53 into prime parts
1084 = third spoke of a hexagonal spiral,[68] 108464 + 1 is prime
1085 = number of partitions of n into distinct parts > or = 2[69]
1086 = Smith number,[70] sum of totient function for first 59 integers
1087 = super-prime, cousin prime, lucky prime[71]
1088 = octo-triangular number, (triangular number result being 136)[72] sum of two distinct powers of 2, (1024 + 64)[73] number that is divisible by exactly seven primes with the inclusion of multiplicity[74]
1089 = 332, nonagonal number, centered octagonal number, first natural number whose digits in its decimal representation get reversed when multiplied by 9.[75]
1090 = sum of 5 positive 5th powers[76]
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[77]), twin prime with 1091 and star number[78]
1094 = sum of 9 positive 5th powers,[59] 109464 + 1 is prime
1095 = sum of 10 positive 5th powers,[79] number that is not the sum of two palindromes
1096 = hendecagonal number,[80] number of strict solid partitions of 18[81]
1097 = emirp[58]
1098 = multiple of 9 containing digit 9 in its base-10 representation[82]
1099 = number where 9 outnumbers every other digit[83]

### 1100 to 1199

1100 = number of partitions of 61 into distinct squarefree parts[84]
1101 = pinwheel number[85]
1102 = sum of totient function for first 60 integers
1103 = Sophie Germain prime,[11] balanced prime[86]
1104 = Keith number[87]
1105 = 332 + 42 = 322 + 92 = 312 + 122 = 232 + 242, Carmichael number,[88] magic constant of n × n normal magic square and n-queens problem for n = 13, decagonal number,[89] centered square number,[12] Fermat pseudoprime[90]
1106 = number of regions into which the plane is divided when drawing 24 ellipses[91]
1107 = number of non-isomorphic strict T0 multiset partitions of weight 8[92]
1108 = number k such that k64 + 1 is prime
1109 = Friedlander-Iwaniec prime[93]
1110 = k such that 2k + 3 is prime[94]
1111 = repdigit
1112 = k such that 9k - 2 is a prime[95]
1113 = number of strict partions of 40[96]
1114 = number of ways to write 22 as an orderless product of orderless sums[97]
1115 = number of partitions of 27 into a prime number of parts[98]
1116 = divisible by the number of primes below it
1117 = number of diagonally symmetric polyominoes with 16 cells[99]
1118 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,21}[100]
1119 = number of bipartite graphs with 9 nodes[101]
1120 = number k such that k64 + 1 is prime
1121 = number of squares between 342 and 344.[102]
1122 = pronic number,[46] divisible by the number of primes below it
1123 = balanced prime[86]
1124 = Leyland number[103]
1125 = Achilles number
1128 = triangular number,[23] hexagonal number,[24] divisible by the number of primes below it
1129 = number of lattice points inside a circle of radius 19[104]
1130 = skiponacci number[105]
1131 = number of edges in the hexagonal triangle T(26)[106]
1134 = divisible by the number of primes below it, triangular matchstick number[107]
1135 = centered triangular number[108]
1136 = number of independent vertex sets and vertex covers in the 7-sunlet graph[109]
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.
1140 = tetrahedral number[110]
1141 = 7-Knödel number[111]
1142 = n such that n32 + 1 is prime[112]
1151 = first prime following a prime gap of 22.[113]
1152 = highly totient number,[114] 3-smooth number (27×32), area of a square with diagonal 48,[49] Achilles number
1153 = super-prime, Proth prime[115]
1154 = 2 × 242 + 2 = number of points on surface of tetrahedron with edgelength 24[116]
1155 = number of edges in the join of two cycle graphs, both of order 33[117]
1156 = 342, octahedral number,[118] centered pentagonal number,[41] centered hendecagonal number.[119]
1158 = number of points on surface of octahedron with edgelength 17[120]
1159 = member of the Mian–Chowla sequence,[15] a centered octahedral number[121]
1160 = octagonal number[122]
1161 = sum of the first 26 primes
1162 = pentagonal number,[65] sum of totient function for first 61 integers
1163 = smallest prime > 342.[123] See Legendre's conjecture.
1166 = heptagonal pyramidal number[124]
1169 = highly cototient number[38]
1170 = highest possible score in a National Academic Quiz Tournaments (NAQT) match
1171 = super-prime
1174 = number of widely totally strongly normal compositions of 16
1176 = triangular number[23]
1177 = heptagonal number[60]
1178 = number of cubes of edge length 1 required to make a hollow cube of edge length 15
1183 = pentagonal pyramidal number
1184 = amicable number with 1210[125]
1185 = number of partitions of 45 into pairwise relatively prime parts[126]
1186 = number of diagonally symmetric polyominoes with 15 cells,[127] number of partitions of 54 into prime parts
1187 = safe prime,[18] Stern prime,[128] balanced prime[86]
1189 = number of squares between 352 and 354.[129]
1190 = pronic number[46]
1191 = 352 - 35 + 1 = H35 (the 35th Hogben number)[130]
1192 = sum of totient function for first 62 integers
1193 = a number such that 41193 - 31193 is prime
1197 = pinwheel number[131]
1198 = centered heptagonal number[61]

### 1200 to 1299

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,[132] number k such that k64 + 1 is prime
1201 = centered square number,[12] super-prime, centered decagonal number
1205 = number of partitions of 28 such that the number of odd parts is a part[133]
1210 = amicable number with 1184[134]
1213 = emirp
1214 = sum of first 39 composite numbers[135]
1215 = number of edges in the hexagonal triangle T(27)[136]
1216 = nonagonal number[137]
1217 = super-prime, Proth prime[115]
1218 = triangular matchstick number[107]
1219 = Mertens function zero, centered triangular number[138]
1220 = Mertens function zero, number of binary vectors of length 16 containing no singletons[139]
1222 = hexagonal pyramidal number
1223 = Sophie Germain prime,[11] balanced prime, 200th prime number[86]
1224 = number of edges in the join of two cycle graphs, both of order 34[140]
1225 = 352, square triangular number,[141] hexagonal number,[24] centered octagonal number[142]
1228 = sum of totient function for first 63 integers
1229 = Sophie Germain prime,[11] number of primes between 0 and 10000
1230 = the Mahonian number: T(9, 6)[143]
1233 = 122 + 332
1234 = number of parts in all partitions of 30 into distinct parts[144]
1236 = 617 + 619: sum of twin prime pair[145]
1237 = prime of the form 2p-1
1238 = number of partitions of 31 that do not contain 1 as a part[29]
1240 = square pyramidal number[14]
1241 = centered cube number[146]
1242 = decagonal number[89]
1244 = number of complete partitions of 25[147]
1247 = pentagonal number[65]
1249 = emirp, trimorphic number[148]
1250 = area of a square with diagonal 50[49]
1251 = 2 × 252 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 25[149]
1252 = 2 × 252 + 2 = number of points on surface of tetrahedron with edgelength 25[150]
1253 = number of partitions of 23 with at least one distinct part[151]
1255 = Mertens function zero, number of ways to write 23 as an orderless product of orderless sums,[152] number of partitions of 23[153]
1256 = Mertens function zero
1257 = number of lattice points inside a circle of radius 20[154]
1258 = Mertens function zero
1259 = highly cototient number[38]
1260 = highly composite number,[155] pronic number,[46] the smallest vampire number,[156] sum of totient function for first 64 integers, number of strict partions of 41[157] and appears twice in the Book of Revelation
1261 = star number,[78] Mertens function zero
1262 = maximal number of regions the plane is divided into by drawing 36 circles[158]
1264 = sum of the first 27 primes
1266 = centered pentagonal number,[41] Mertens function zero
1267 = 7-Knödel number[159]
1268 = number of partitions of 37 into prime power parts[160]
1270 = Mertens function zero
1271 = sum of first 40 composite numbers[161]
1274 = sum of the nontriangular numbers between successive triangular numbers
1275 = triangular number,[23] sum of the first 50 natural numbers
1279 = Mertens function zero, Mersenne prime exponent
1280 = Mertens function zero, number of parts in all compositions of 9.[162]
1281 = octagonal number[163]
1282 = Mertens function zero, number of partitions of 46 into pairwise relatively prime parts[164]
1283 = safe prime[18]
1284 = 641 + 643: sum of twin prime pair[165]
1285 = Mertens function zero, number of free nonominoes, number of parallelogram polyominoes with 10 cells.[166]
1288 = heptagonal number[60]
1289 = Sophie Germain prime,[11] Mertens function zero
1291 = Mertens function zero
1292 = Mertens function zero
1295 = number of edges in the join of two cycle graphs, both of order 35[167]
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[168]
1298 = number of partitions of 55 into prime parts
1299 = Mertens function zero

### 1300 to 1399

1300 = Sum of the first 4 fifth powers, mertens function zero, largest possible win margin in an NAQT match
1301 = centered square number,[12] Honaker prime[169]
1302 = Mertens function zero, number of edges in the hexagonal triangle T(28)[170]
1305 = triangular matchstick number[107]
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.[171]
1307 = safe prime[18]
1308 = sum of totient function for first 65 integers
1309 = the first sphenic number followed by two consecutive such number
1312 = member of the Mian-Chowla sequence;[15] code for "ACAB" itself an acronym for "all cops are bastards"[172]
1314 = number of integer partitions of 41 whose distinct parts are connected[173]
1318 = Mertens function zero
1319 = safe prime[18]
1320 = 659 + 661: sum of twin prime pair[174]
1323 = Achilles number
1325 = Markov number[175]
1326 = triangular number,[23] hexagonal number,[24] 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[176]
1330 = tetrahedral number,[103] forms a Ruth–Aaron pair with 1331 under second definition
1331 = 113, centered heptagonal number,[61] 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[46]
1333 = 372 - 37 + 1 = H37 (the 37th Hogben number)[177]
1334 = maximal number of regions the plane is divided into by drawing 37 circles[178]
1335 = pentagonal number,[65] Mertens function zero
1336 = Mertens function zero
1337 = Used in the novel form of spelling called leet. Approximate melting point of gold in kelvins.
1338 = Mertens function zero
1340 = k such that 5 × 2k - 1 is prime[179]
1342 = Mertens function zero
1343 = cropped hexagone[180]
1349 = Stern-Jacobsthal number[181]
1350 = nonagonal number[137]
1351 = number of partitions of 28 into a prime number of parts[182]
1352 = number of cubes of edge length 1 required to make a hollow cube of edge length 16, Achilles number
1353 = 2 × 262 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 26[183]
1354 = 2 × 262 + 2 = number of points on surface of tetrahedron with edgelength 26[184]
1361 = first prime following a prime gap of 34,[113] centered decagonal number, Honaker prime[185]
1365 = pentatope number[186]
1367 = safe prime,[18] 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),[86]
1368 = number of edges in the join of two cycle graphs, both of order 36[187]
1369 = 372, centered octagonal number[142]
1371 = sum of the first 28 primes
1372 = Achilles number
1373 = number of lattice points inside a circle of radius 21[188]
1374 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,23}[189]
1375 = decagonal pyramidal number[190]
1376 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)[191]
1378 = triangular number[23]
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[192]
1381 = centered pentagonal number[41]
1386 = octagonal pyramidal number[193]
1387 = 5th Fermat pseudoprime of base 2,[194] 22nd centered hexagonal number and the 19th decagonal number,[89] second Super-Poulet number.[195]
1389 = sum of first 42 composite numbers[196]
1392 = number of edges in the hexagonal triangle T(29)[197]
1393 = 7-Knödel number[198]
1394 = sum of totient function for first 67 integers
1395 = vampire number,[156] member of the Mian–Chowla sequence[15] triangular matchstick number[107]
1396 = centered triangular number[199]
1398 = number of integer partitions of 40 whose distinct parts are connected[200]

### 1400 to 1499

1400 = number of sum-free subsets of {1, ..., 15}[201]
1401 = pinwheel number[202]
1404 = heptagonal number[60]
1405 = 262 + 272, 72 + 82 + ... + 162, centered square number[12]
1406 = pronic number,[46] semi-meandric number[203]
1407 = 382 - 38 + 1 = H38 (the 38th Hogben number)[204]
1408 = maximal number of regions the plane is divided into by drawing 38 circles[205]
1409 = super-prime, Sophie Germain prime,[11] smallest number whose eighth power is the sum of 8 eighth powers, Proth prime[115]
1415 = the Mahonian number: T(8, 8)[206]
1419 = Zeisel number[207]
1420 = Number of partitions of 56 into prime parts
1425 = self-descriptive number in base 5
1426 = sum of totient function for first 68 integers, pentagonal number,[65] number of strict partions of 42[208]
1430 = Catalan number[209]
1431 = triangular number,[23] hexagonal number[24]
1432 = member of Padovan sequence[66]
1433 = super-prime, Honaker prime,[210] typical port used for remote connections to Microsoft SQL Server databases
1435 = vampire number;[156] the standard railway gauge in millimetres, equivalent to 4 feet 8+12 inches (1.435 m)
1438 = k such that 5 × 2k - 1 is prime[211]
1439 = Sophie Germain prime,[11] safe prime[18]
1440 = a highly totient number[114] 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[78]
1442 = number of parts in all partitions of 31 into distinct parts[212]
1443 = number of edges in the join of two cycle graphs, both of order 37[213]
1444 = 382, smallest pandigital number in Roman numerals
1446 = number of points on surface of octahedron with edgelength 19[214]
1447 = super-prime, happy number
1449 = Stella octangula number
1451 = Sophie Germain prime[11]
1453 = Sexy prime with 1459
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 = Nickname of the original "Doc Marten's" boots, released 1 April 1960
1461 = number of partitions of 38 into prime power parts[215]
1463 = total number of parts in all partitions of 16[216]
1469 = octahedral number,[118] highly cototient number[38]
1470 = pentagonal pyramidal number,[217] sum of totient function for first 69 integers
1471 = super-prime, centered heptagonal number[61]
1473 = cropped hexagone[218]
1476 = coreful perfect number[219]
1477 = 7-Knödel number[220]
1479 = number of planar partitions of 12[221]
1480 = sum of the first 29 primes
1481 = Sophie Germain prime[11]
1482 = pronic number,[46] number of unimodal compositions of 15 where the maximal part appears once[222]
1483 = 392 - 39 + 1 = H39 (the 39th Hogben number)[223]
1484 = maximal number of regions the plane is divided into by drawing 39 circles[224]
1485 = triangular number
1486 = number of strict solid partitions of 19[225]
1487 = safe prime[18]
1488 = triangular matchstick number[107]
1489 = centered triangular number[226]
1490 = tetranacci number[227]
1491 = nonagonal number,[137] Mertens function zero
1492 = Mertens function zero
1493 = Stern prime[128]
1494 = sum of totient function for first 70 integers
1496 = square pyramidal number[14]
1497 = skiponacci number[228]
1498 = number of flat partitions of 41[229]
1499 = Sophie Germain prime,[11] super-prime

### 1500 to 1599

1501 = centered pentagonal number[41]
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[230]
1504 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)[231]
1507 = number of partitions of 32 that do not contain 1 as a part[29]
1508 = heptagonal pyramidal number[232]
1509 = pinwheel number[233]
1510 = deficient number, odious number
1511 = Sophie Germain prime,[11] balanced prime[86]
1513 = centered square number[12]
1514 = sum of first 44 composite numbers[234]
1517 = number of lattice points inside a circle of radius 22[235]
1518 = Mertens function zero
1519 = Mertens function zero
1520 = pentagonal number,[65] Mertens function zero, forms a Ruth–Aaron pair with 1521 under second definition
1521 = 392, Mertens function zero, centered octagonal number,[142] forms a Ruth–Aaron pair with 1520 under second definition
1522 = k such that 5 × 2k - 1 is prime[236]
1523 = super-prime, Mertens function zero, safe prime,[18] member of the Mian–Chowla sequence[15]
1524 = Mertens function zero
1525 = heptagonal number,[60] Mertens function zero
1526 = number of conjugacy classes in the alternating group A27[237]
1527 = Mertens function zero
1528 = Mertens function zero
1530 = vampire number[156]
1531 = centered decagonal number, Mertens function zero
1532 = Mertens function zero
1535 = Thabit number
1536 = a common size of microplate, 3-smooth number (29×3), number of threshold functions of exactly 4 variables[238]
1537 = Keith number,[87] Mertens function zero
1538 = number of surface points on a cube with edge-length 17[239]
1540 = triangular number, hexagonal number,[24] decagonal number,[89] tetrahedral number[103]
1541 = octagonal number[240]
1543 = Mertens function zero
1544 = Mertens function zero, number of partitions of integer partitions of 17 where all parts have the same length[241]
1546 = Mertens function zero
1547 = hexagonal pyramidal number
1548 = coreful perfect number[242]
1552 = Number of partitions of 57 into prime parts
1556 = sum of the squares of the first nine primes
1558 = number k such that k64 + 1 is prime
1559 = Sophie Germain prime[11]
1560 = pronic number[46]
1561 = a centered octahedral number,[121] number of series-reduced trees with 19 nodes[243]
1562 = maximal number of regions the plane is divided into by drawing 40 circles[244]
1564 = sum of totient function for first 71 integers
1566 = number k such that k64 + 1 is prime
1567 = number of partitions of 24 with at least one distinct part[245]
1568 = Achilles number[246]
1569 = 2 × 282 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 28[247]
1570 = 2 × 282 + 2 = number of points on surface of tetrahedron with edgelength 28[248]
1571 = Honaker prime[249]
1572 = member of the Mian–Chowla sequence[15]
1575 = odd abundant number,[250] sum of the nontriangular numbers between successive triangular numbers, number of partitions of 24[251]
1578 = sum of first 45 composite numbers[252]
1581 = number of edges in the hexagonal triangle T(31)[253]
1583 = Sophie Germain prime
1584 = triangular matchstick number[107]
1585 = Riordan number, centered triangular number[254]
1588 = sum of totient function for first 72 integers
1593 = sum of the first 30 primes
1595 = number of non-isomorphic set-systems of weight 10
1596 = triangular number
1597 = Fibonacci prime,[255] Markov prime,[175] super-prime, emirp
1598 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,25}[256]
1599 = number of edges in the join of two cycle graphs, both of order 39[257]

### 1600 to 1699

1600 = 402, 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 2005-2015)
1601 = Sophie Germain prime, Proth prime,[115] the novel 1601 (Mark Twain)
1602 = number of points on surface of octahedron with edgelength 20[258]
1603 = number of partitions of 27 with nonnegative rank[259]
1606 = enneagonal pyramidal number[260]
1609 = cropped hexagone[261]
1610 = number of strict partions of 43[262]
1617 = pentagonal number[65]
1618 = centered heptagonal number[61]
1619 = palindromic prime in binary, safe prime[18]
1620 = 809 + 811: sum of twin prime pair[263]
1621 = super-prime, pinwheel number[264]
1625 = centered square number[12]
1626 = centered pentagonal number[41]
1630 = number k such that k^64 + 1 is prime
1633 = star number[78]
1634 = Narcissistic number in base 10
1638 = harmonic divisor number,[265] 5 × 21638 - 1 is prime[266]
1639 = nonagonal number[137]
1640 = pronic number[46]
1641 = 412 - 41 + 1 = H41 (the 41st Hogben number)[267]
1642 = maximal number of regions the plane is divided into by drawing 41 circles[268]
1643 = sum of first 46 composite numbers[269]
1644 = 821 + 823: sum of twin prime pair[270]
1649 = highly cototient number,[38] Leyland number[103]
1651 = heptagonal number[60]
1652 = number of partitions of 29 into a prime number of parts[271]
1653 = triangular number, hexagonal number,[24] number of lattice points inside a circle of radius 23[272]
1656 = 827 + 829: sum of twin prime pair[273]
1657 = cuban prime,[274] prime of the form 2p-1
1660 = sum of totient function for first 73 integers
1662 = number of partitions of 49 into pairwise relatively prime parts[275]
1666 = largest efficient pandigital number in Roman numerals (each symbol occurs exactly once)
1669 = super-prime
1678 = n such that n32 + 1 is prime[276]
1679 = highly cototient number,[38] semiprime (23 × 73, see also Arecibo message), number of parts in all partitions of 32 into distinct parts[277]
1680 = highly composite number,[155] number of edges in the join of two cycle graphs, both of order 40[278]
1681 = 412, smallest number yielded by the formula n2 + n + 41 that is not a prime; centered octagonal number[142]
1682 = and 1683 is a member of a Ruth–Aaron pair (first definition)
1683 = triangular matchstick number[107]
1684 = centered triangular number[279]
1687 = 7-Knödel number[280]
1692 = coreful perfect number[281]
1693 = smallest prime > 412.[282]
1694 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,26}[283]
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

### 1700 to 1799

1701 = ${\displaystyle \left\{{8 \atop 4}\right\}}$ , decagonal number, hull number of the U.S.S. Enterprise on Star Trek
1702 = palindromic in 3 consecutive bases: 89814, 78715, 6A616
1705 = tribonacci number[284]
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
1711 = triangular number, centered decagonal number
1716 = 857 + 859: sum of twin prime pair[285]
1717 = pentagonal number[65]
1720 = sum of the first 31 primes
1721 = number of squares between 422 and 424.[286]
1722 = Giuga number,[287] pronic number[46]
1723 = super-prime
1724 = maximal number of regions the plane is divided into by drawing 42 circles[288]
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.
1733 = Sophie Germain prime, palindromic in bases 3, 18, 19.
1736 = sum of totient function for first 75 integers, number of surface points on a cube with edge-length 18[289]
1737 = pinwheel number[290]
1741 = super-prime, centered square number[12]
1747 = balanced prime[86]
1751 = cropped hexagone[291]
1753 = balanced prime[86]
1754 = k such that 5*2k - 1 is prime[292]
1756 = centered pentagonal number[41]
1760 = the number of yards in a mile
1763 = number of edges in the join of two cycle graphs, both of order 41[293]
1764 = 422
1766 = number of points on surface of octahedron with edgelength 21[294]
1770 = triangular number, hexagonal number,[24] Town of Seventeen Seventy in Australia
1771 = tetrahedral number[103]
1772 = centered heptagonal number,[61] sum of totient function for first 76 integers
1777 = smallest prime > 422.[295]
1782 = heptagonal number[60]
1785 = square pyramidal number,[14] triangular matchstick number[107]
1786 = centered triangular number[296]
1787 = super-prime, sum of eleven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191)
1790 = number of partitions of 50 into pairwise relatively prime parts[297]
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[298]
1794 = nonagonal number,[137] number of partitions of 33 that do not contain 1 as a part[29]

### 1800 to 1899

1800 = pentagonal pyramidal number,[217] 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)[274]
1802 = 2 × 302 + 2 = number of points on surface of tetrahedron with edgelength 30,[299] number of partitions of 30 such that the number of odd parts is a part[300]
1804 = number k such that k^64 + 1 is prime
1805 = number of squares between 432 and 434.[301]
1806 = pronic number,[46] product of first four terms of Sylvester's sequence, primary pseudoperfect number,[302] only number for which n equals the denominator of the nth Bernoulli number,[303] Schröder number[304]
1807 = fifth term of Sylvester's sequence[305]
1808 = maximal number of regions the plane is divided into by drawing 43 circles[306]
1811 = Sophie Germain prime
1812 = n such that n32 + 1 is prime[307]
1816 = number of strict partions of 44[308]
1818 = n such that n32 + 1 is prime[309]
1820 = pentagonal number,[65] pentatope number,[186] number of compositions of 13 whose run-lengths are either weakly increasing or weakly decreasing[19]
1821 = member of the Mian–Chowla sequence[15]
1822 = number of integer partitions of 43 whose distinct parts are connected[310]
1823 = super-prime, safe prime[18]
1825 = octagonal number[311]
1826 = decagonal pyramidal number[312]
1827 = vampire number[156]
1828 = meandric number, open meandric number, appears twice in the first 10 decimal digits of e
1830 = triangular number
1832 = sum of totient function for first 77 integers
1834 = octahedral number,[118] sum of the cubes of the first five primes
1836 = factor by which a proton is more massive than an electron
1837 = star number[78]
1838 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,27}[313]
1841 = Mertens function zero
1843 = Mertens function zero
1844 = Mertens function zero
1845 = Mertens function zero
1846 = sum of first 49 composite numbers[314]
1847 = super-prime
1848 = number of edges in the join of two cycle graphs, both of order 42[315]
1849 = 432, palindromic in base 6 (= 123216), centered octagonal number[142]
1850 = Number of partitions of 59 into prime parts
1851 = sum of the first 32 primes
1853 = Mertens function zero
1854 = Mertens function zero
1856 = sum of totient function for first 78 integers
1857 = Mertens function zero, pinwheel number[316]
1861 = centered square number,[12] 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
1866 = Mertens function zero
1870 = decagonal number[89]
1876 = number k such that k^64 + 1 is prime
1878 = n such that n32 + 1 is prime[317]
1879 = a prime with square index[318]
1880 = the 10th element of the self convolution of Lucas numbers[319]
1881 = tricapped prism number[320]
1882 = number of linearly separable boolean functions in 4 variables[321]
1883 = number of conjugacy classes in the alternating group A28[322]
1884 = k such that 5*2k - 1 is prime[323]
1885 = Zeisel number[207]
1886 = number of partitions of 64 into fourth powers[324]
1887 = number of edges in the hexagonal triangle T(34)[325]
1888 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)[326]
1889 = Sophie Germain prime, highly cototient number[38]
1890 = triangular matchstick number[107]
1891 = triangular number, hexagonal number,[24] centered pentagonal number,[41] centered triangular number[327]
1892 = pronic number[46]
1893 = 442 - 44 + 1 = H44 (the 44th Hogben number)[328]
1894 = maximal number of regions the plane is divided into by drawing 44 circles[329]
1895 = Stern-Jacobsthal number[330]
1896 = member of the Mian-Chowla sequence[15]
1897 = member of Padovan sequence,[66] number of triangle-free graphs on 9 vertices[331]
1898 = smallest multiple of n whose digits sum to 26[332]
1899 = cropped hexagone[333]

### 1900 to 1999

1900 = number of primes <= 214.[20] Also 1900 (film) or Novecento, 1976 movie
1901 = Sophie Germain prime, centered decagonal number
1902 = number of symmetric plane partitions of 27[334]
1903 = generalized catalan number[335]
1904 = number of flat partitions of 43[336]
1905 = Fermat pseudoprime[337]
1906 = number n such that 3n - 8 is prime[338]
1907 = safe prime,[18] balanced prime[86]
1908 = coreful perfect number[339]
1909 = hyperperfect number[340]
1910 = number of compositions of 13 having exactly one fixed point[341]
1911 = heptagonal pyramidal number[342]
1912 = size of 6th maximum raising after one blind in pot-limit poker[343]
1913 = super-prime, Honaker prime[344]
1914 = number of bipartite partitions of 12 white objects and 3 black ones[345]
1915 = number of nonisomorphic semigroups of order 5[346]
1916 = sum of first 50 composite numbers[347]
1917 = number of partitions of 51 into pairwise relatively prime parts[348]
1918 = heptagonal number[60]
1919 = smallest number with reciprocal of period length 36 in base 10[349]
1920 = sum of the nontriangular numbers between successive triangular numbers
1921 = 4-dimensional centered cube number[350]
1922 = Area of a square with diagonal 62[351]
1923 = 2 × 312 + 1 = number of different 2 X 2 determinants with integer entries from 0 to 31[352]
1924 = 2 × 312 + 2 = number of points on surface of tetrahedron with edgelength 31[353]
1925 = number of ways to write 24 as an orderless product of orderless sums[354]
1926 = pentagonal number[65]
1927 = 211 - 112[355]
1928 = number of distinct values taken by 2^2^...^2 (with 13 2's and parentheses inserted in all possible ways)[356]
1929 = Mertens function zero, number of integer partitions of 42 whose distinct parts are connected[357]
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[358]
1931 = Sophie Germain prime
1932 = number of partitions of 40 into prime power parts[359]
1933 = centered heptagonal number,[61] Honaker prime[360]
1934 = sum of totient function for first 79 integers
1935 = number of edges in the join of two cycle graphs, both of order 43[361]
1936 = 442, 18-gonal number,[362] 324-gonal number.
1937 = number of chiral n-ominoes in 12-space, one cell labeled[363]
1938 = Mertens function zero, number of points on surface of octahedron with edgelength 22[364]
1939 = 7-Knödel number[365]
1940 = the Mahonian number: T(8, 9)[366]
1941 = maximal number of regions obtained by joining 16 points around a circle by straight lines[367]
1942 = number k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes[368]
1943 = largest number not the sum of distinct tetradecagonal numbers[369]
1944 = 3-smooth number (23×35), Achilles number[370]
1945 = number of partitions of 25 into relatively prime parts such that multiplicities of parts are also relatively prime[371]
1946 = number of surface points on a cube with edge-length 19[372]
1947 = k such that 5·2k + 1 is a prime factor of a Fermat number 22m + 1 for some m[373]
1948 = number of strict solid partitions of 20[374]
1949 = smallest prime > 442.[375]
1950 = ${\displaystyle 1\cdot 2\cdot 3+4\cdot 5\cdot 6+7\cdot 8\cdot 9+10\cdot 11\cdot 12}$ ,[376] largest number not the sum of distinct pentadecagonal numbers[377]
1951 = cuban prime[274]
1952 = number of covers of {1, 2, 3, 4}[378]
1953 = triangular number
1956 = number of sum-free subsets of {1, ..., 16}[379]
1955 = number of partitions of 25 with at least one distinct part[380]
1956 = nonagonal number[137]
1957 = ${\displaystyle \sum _{k=0}^{6}{\frac {6!}{k!}}}$  = total number of ordered k-tuples (k=0,1,2,3,4,5,6) of distinct elements from an 6-element set[381]
1958 = number of partitions of 25[382]
1959 = Heptanacci-Lucas number[383]
1960 = number of parts in all partitions of 33 into distinct parts[384]
1961 = number of lattice points inside a circle of radius 25[385]
1962 = number of edges in the join of the complete graph K36 and the cycle graph C36[386]
1963! - 1 is prime[387]
1964 = number of linear forests of planted planar trees with 8 nodes[388]
1965 = total number of parts in all partitions of 17[389]
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[390]
σ(1968) = σ(1967) + σ(1966)[391]
1969 = Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize[392]
1970 = number of compositions of two types of 9 having no even parts[393]
1971 = ${\displaystyle 3^{7}-6^{3}}$ [394]
1972 = n such that ${\displaystyle {\frac {n^{37}-1}{n-1}}}$  is prime[395]
1973 = Sophie Germain prime, Leonardo prime
1974 = number of binary vectors of length 17 containing no singletons[396]
1975 = number of partitions of 28 with nonnegative rank[397]
1976 = octagonal number[398]
1977 = number of non-isomorphic multiset partitions of weight 9 with no singletons[399]
1978 = n such that n | (3n + 5)[400]
1979 = number of squares between 452 and 454.[401]
1980 = pronic number[46]
1981 = pinwheel number[402]
1982 = maximal number of regions the plane is divided into by drawing 45 circles[403]
1983 = skiponacci number[404]
1985 = centered square number[12]
1986 = number of ways to write 25 as an orderless product of orderless sums[405]
1987 = 300th prime number
1988 = sum of the first 33 primes
1989 = number of 9-step mappings with 4 inputs[406]
1990 = Stella octangula number
1991 = the 46th Gullwing number[407]
1992 = number of nonisomorphic sets of nonempty subsets of a 4-set[408]
1993 = a number with the property that 41993 - 31993 is prime,[409] number of partitions of 30 into a prime number of parts[410]
1994 = Glaisher's function W(37)[411]
1995 = number of unlabeled graphs on 9 vertices with independence number 6[412]
1996 = a number with the property that (1996! + 3)/3 is prime[413]
1997 = ${\displaystyle \sum _{k=1}^{21}{k\cdot \phi (k)}}$ [414]
1998 = triangular matchstick number[107]
1999 = centered triangular number[415]

### Prime numbers

There are 135 prime numbers between 1000 and 2000:[416][417]

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

## References

1. ^ "chiliad". Merriam-Webster. Archived from the original on March 25, 2022.
2. ^ "Factors of 1000". Gcf & Lwcm. Archived from the original on 2020-11-05. Retrieved October 25, 2020.
3. ^ "1000". Prime Curious!. Archived from the original on March 25, 2022.
4. ^ "Sloane's A122189 : Heptanacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on October 7, 2016. Retrieved July 13, 2017.
5. ^ Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
6. ^ a b
7. ^
8. ^ Sloane, N. J. A. (ed.). "Sequence A034262". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
9. ^ a b Sloane, N. J. A. (ed.). "Sequence A020473". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
10. ^
11. "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2015. Retrieved June 12, 2016.
12. "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2015. Retrieved June 12, 2016.
13. ^ Sloane, N. J. A. (ed.). "Sequence A000325". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
14. ^ a b c d "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
15. "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on May 17, 2016. Retrieved June 12, 2016.
16. ^
17. ^ 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 2022-05-24.
18. "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
19. ^ a b 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 2022-06-02.
20. ^ a b Sloane, N. J. A. (ed.). "Sequence A007053". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
21. ^ Richard Kenneth Guy (June 29, 2013). "A. Prime numbers". Unsolved Problems in Number Theory. Springer Science+Business Media. p. 7. ISBN 978-1475717389. Archived from the original on March 25, 2022.
22. ^
23. "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on April 5, 2016. Retrieved June 12, 2016.
24. "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on April 17, 2016. Retrieved June 12, 2016.
25. ^ a b
26. ^
27. ^
28. ^
29. ^ 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 2022-06-02.
30. ^ a b
31. ^
32. ^ a b
33. ^
34. ^
35. ^
36. ^
37. ^
38. "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
39. ^
40. ^
41. "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
42. ^
43. ^
44. ^
45. ^
46. "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 9, 2016. Retrieved June 12, 2016.
47. ^
48. ^
49. ^ a b c Sloane, N. J. A. (ed.). "Sequence A001105". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
50. ^
51. ^ a b c
52. ^ "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 March 25, 2022. Retrieved January 19, 2022.
53. ^
54. ^
55. ^
56. ^
57. ^
58. ^ a b
59. ^ a b
60. "Sloane's A000566 : Heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2016. Retrieved June 12, 2016.
61. "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 9, 2016. Retrieved June 12, 2016.
62. ^
63. ^
64. ^
65. "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
66. ^ a b c "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
67. ^
68. ^
69. ^
70. ^ "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 9, 2016. Retrieved June 12, 2016.
71. ^ "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on March 4, 2016. Retrieved June 12, 2016.
72. ^
73. ^
74. ^
75. ^ "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 October 17, 2015. Retrieved June 14, 2016.
76. ^
77. ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 163
78. "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2016. Retrieved June 12, 2016.
79. ^
80. ^
81. ^ Sloane, N. J. A. (ed.). "Sequence A323657 (Number of strict solid partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
82. ^
83. ^
84. ^
85. ^ Sloane, N. J. A. (ed.). "Sequence A059993". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
86. "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
87. ^ a b "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
88. ^ "Sloane's A002997 : Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
89. "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
90. ^
91. ^ Sloane, N. J. A. (ed.). "Sequence A051890 (2*(n^2 - n + 1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
92. ^
93. ^
94. ^ 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.
95. ^ 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.
96. ^
97. ^
98. ^
99. ^
100. ^
101. ^ Sloane, N. J. A. (ed.). "Sequence A033995 (Number of bipartite graphs with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
102. ^ Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
103. "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
104. ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
105. ^ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
106. ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
107. Sloane, N. J. A. (ed.). "Sequence A045943". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
108. ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
109. ^ Sloane, N. J. A. (ed.). "Sequence A080040". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
110. ^ "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
111. ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
112. ^ 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.
113. ^ a b "Sloane's A000101 : Increasing gaps between primes (upper end)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-07-10.
114. ^ a b "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
115. ^ a b c d "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
116. ^
117. ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
118. ^ a b c "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
119. ^ "Sloane's A069125 : a(n) = (11*n^2 - 11*n + 2)/2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
120. ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
121. ^ 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 2022-06-02.
122. ^
123. ^ Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
124. ^ Sloane, N. J. A. (ed.). "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
125. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
126. ^
127. ^
128. ^ a b "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
129. ^ Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
130. ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
131. ^ Sloane, N. J. A. (ed.). "Sequence A059993". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
132. ^ Meehan, Eileen R., Why TV is not our fault: television programming, viewers, and who's really in control Lanham, MD: Rowman & Littlefield, 2005
133. ^
134. ^ Higgins, ibid.
135. ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
136. ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
137. "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
138. ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
139. ^
140. ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
141. ^ "Sloane's A001110 : Square triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
142. "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
143. ^ Sloane, N. J. A. (ed.). "Sequence A008302". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
144. ^
145. ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
146. ^ "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
147. ^ Sloane, N. J. A. (ed.). "Sequence A126796 (Number of complete partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
148. ^ "Sloane's A033819 : Trimorphic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
149. ^ Sloane, N. J. A. (ed.). "Sequence A058331 (2*n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
150. ^
151. ^
152. ^
153. ^
154. ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
155. ^ a b "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
156. "Sloane's A014575 : Vampire numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
157. ^
158. ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
159. ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
160. ^ 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.
161. ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
162. ^ Sloane, N. J. A. (ed.). "Sequence A001792". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
163. ^
164. ^
165. ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
166. ^
167. ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
168. ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
169. ^
170. ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
171. ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
172. ^ "Constitutional Court allows 'FCK CPS' sticker". The Local. 28 April 2015. "...state court in Karlsruhe ruled that a banner ... that read 'ACAB' – an abbreviation of 'all cops are bastards' ... a punishable insult. ... A court in Frankfurt ... the numbers '1312' constituted an insult ... the numerals stand for the letters ACAB's position in the alphabet.
173. ^
174. ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
175. ^ a b "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
176. ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
177. ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
178. ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
179. ^ 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.
180. ^ Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
181. ^ Sloane, N. J. A. (ed.). "Sequence A101624 (Stern-Jacobsthal number)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
182. ^
183. ^ Sloane, N. J. A. (ed.). "Sequence A058331 (2*n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
184. ^
185. ^
186. ^ 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 2016-06-12.
187. ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
188. ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
189. ^
190. ^ Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
191. ^
192. ^ Sloane, N. J. A. (ed.). "Sequence A005945 (Number of n-step mappings with 4 inputs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
193. ^ Sloane, N. J. A. (ed.). "Sequence A002414 (Octagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
194. ^ "Sloane's A001567 : Fermat pseudoprimes to base 2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
195. ^ "Sloane's A050217 : Super-Poulet numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
196. ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
197. ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
198. ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
199. ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
200. ^
201. ^ Sloane, N. J. A. (ed.). "Sequence A007865 (Number of sum-free subsets of {1, ..., n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
202. ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
203. ^ "Sloane's A000682 : Semimeanders". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
204. ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
205. ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
206. ^ Sloane, N. J. A. (ed.). "Sequence A008302". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
207. ^ a b "Sloane's A051015 : Zeisel numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
208. ^
209. ^ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
210. ^
211. ^ 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.
212. ^
213. ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
214. ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
215. ^ 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.
216. ^
217. ^ a b "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
218. ^ Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
219. ^ Sloane, N. J. A. (ed.). "Sequence A307958 (Coreful perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
220. ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
221. ^
222. ^
223. ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
224. ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
225. ^ Sloane, N. J. A. (ed.). "Sequence A323657 (Number of strict solid partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
226. ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
227. ^ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
228. ^ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
229. ^ Sloane, N. J. A. (ed.). "Sequence A034296 (Number of flat partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
230. ^
231. ^
232. ^ Sloane, N. J. A. (ed.). "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
233. ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
234. ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
235. ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
236. ^ 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.
237. ^
238. ^ Sloane, N. J. A. (ed.). functions of exactly n variables "Sequence A000615Threshold functions of exactly n variables". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. {{cite web}}: Check |url= value (help)
239. ^ Sloane, N. J. A. (ed.). "Sequence A005897". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
240. ^
241. ^
242. ^ Sloane, N. J. A. (ed.). "Sequence A307958 (Coreful perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
243. ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
244. ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
245. ^
246. ^ Sloane, N. J. A. (ed.). "Sequence A052486". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
247. ^ Sloane, N. J. A. (ed.). "Sequence A058331 (2*n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
248. ^
249. ^
250. ^ "Sloane's A005231 : Odd abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
251. ^
252. ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
253. ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
254. ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
255. ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
256. ^
257. ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
258. ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
259. ^ Sloane, N. J. A. (ed.). "Sequence A064174 (Number of partitions of n with nonnegative rank)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
260. ^ Sloane, N. J. A. (ed.). "Sequence A007584 (9-gonal (or enneagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
261. ^ Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
262. ^
263. ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
264. ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
265. ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
266. ^ 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.
267. ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
268. ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
269. ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
270. ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
271. ^
272. ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
273. ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
274. ^ a b c "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
275. ^
276. ^ 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.
277. ^
278. ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
279. ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
280. ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
281. ^ Sloane, N. J. A. (ed.). "Sequence A307958 (Coreful perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
282. ^ Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
283. ^
284. ^ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
285. ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
286. ^ Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
287. ^ "Sloane's A007850 : Giuga numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
288. ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
289. ^ Sloane, N. J. A. (ed.). "Sequence A005897". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
290. ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
291. ^ Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
292. ^ 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.
293. ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
294. ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
295. ^ Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
296. ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
297. ^
298. ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
299. ^
300. ^
301. ^ Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
302. ^ "Sloane's A054377 : Primary pseudoperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
303. ^ Kellner, Bernard C.; 'The equation denom(Bn) = n has only one solution'
304. ^ Sloane, N. J. A. (ed.). "Sequence A006318 (Large Schröder numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
305. ^ "Sloane's A000058 : Sylvester's sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
306. ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
307. ^ 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.
308. ^
309. ^ 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.
310. ^
311. ^
312. ^ Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
313. ^
314. ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
315. ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
316. ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
317. ^ 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.
318. ^ Sloane, N. J. A. (ed.). "Sequence A011757 (prime(n^2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
319. ^ Sloane, N. J. A. (ed.). "Sequence A004799 (Self convolution of Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
320. ^ Sloane, N. J. A. (ed.). "Sequence A005920 (Tricapped prism numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
321. ^
322. ^
323. ^ 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.
324. ^ 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.
325. ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
326. ^
327. ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
328. ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
329. ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
330. ^ Sloane, N. J. A. (ed.). "Sequence A101624 (Stern-Jacobsthal number)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
331. ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
332. ^ 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.
333. ^ Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
334. ^ Sloane, N. J. A. (ed.). "Sequence A005987 (Number of symmetric plane partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
335. ^ Sloane, N. J. A. (ed.). "Sequence A023431 (Generalized Catalan Numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
336. ^ Sloane, N. J. A. (ed.). "Sequence A034296 (Number of flat partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
337. ^
338. ^ 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.
339. ^ Sloane, N. J. A. (ed.). "Sequence A307958 (Coreful perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
340. ^ "Sloane's A034897 : Hyperperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
341. ^
342. ^ Sloane, N. J. A. (ed.). "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
343. ^ Sloane, N. J. A. (ed.). "Sequence A007070 (4*a(n-1) - 2*a(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
344. ^
345. ^
346. ^ Sloane, N. J. A. (ed.). "Sequence A027851 (Number of nonisomorphic semigroups of order n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
347. ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
348. ^
349. ^
350. ^ Sloane, N. J. A. (ed.). "Sequence A008514 (4-dimensional centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
351. ^ Sloane, N. J. A. (ed.). "Sequence A001105 (2*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
352. ^ Sloane, N. J. A. (ed.). "Sequence A058331 (2*n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
353. ^
354. ^
355. ^ Sloane, N. J. A. (ed.). "Sequence A024012 (2^n - n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
356. ^
357. ^
358. ^
359. ^ 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.
360. ^
361. ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
362. ^ "Sloane's A051870 : 18-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
363. ^
364. ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
365. ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
366. ^ Sloane, N. J. A. (ed.). "Sequence A008302". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
367. ^
368. ^
369. ^
370. ^ Sloane, N. J. A. (ed.). "Sequence A052486". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
371. ^
372. ^ Sloane, N. J. A. (ed.). "Sequence A005897". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
373. ^
374. ^ Sloane, N. J. A. (ed.). "Sequence A323657 (Number of strict solid partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
375. ^ Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
376. ^
377. ^
378. ^ Sloane, N. J. A. (ed.). "Sequence A055621 (Number of covers of an unlabeled n-set)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
379. ^ Sloane, N. J. A. (ed.). "Sequence A007865 (Number of sum-free subsets of {1, ..., n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
380. ^
381. ^
382. ^
383. ^ Sloane, N. J. A. (ed.). "Sequence A104621 (Heptanacci-Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
384. ^
385. ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
386. ^ Sloane, N. J. A. (ed.). "Sequence A005449 (Second pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
387. ^ Sloane, N. J. A. (ed.). "Sequence A002982 (Numbers n such that n! - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
388. ^
389. ^
390. ^
391. ^
392. ^ Jon Froemke & Jerrold W. Grossman (Feb 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.
393. ^ Sloane, N. J. A. (ed.). "Sequence A052542 (2*a(n-1) + a(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
394. ^ Sloane, N. J. A. (ed.). "Sequence A024069 (6^n - n^7)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
395. ^ 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.
396. ^
397. ^ Sloane, N. J. A. (ed.). "Sequence A064174 (Number of partitions of n with nonnegative rank)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
398. ^
399. ^
400. ^ Sloane, N. J. A. (ed.). "Sequence A277288 (Positive integers n such that n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
401. ^ Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
402. ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
403. ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
404. ^ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
405. ^
406. ^ Sloane, N. J. A. (ed.). "Sequence A005945 (Number of n-step mappings with 4 inputs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
407. ^ Sloane, N. J. A. (ed.). "Sequence A187220 (Gullwing sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
408. ^
409. ^
410. ^
411. ^ Sloane, N. J. A. (ed.). "Sequence A002470 (Glaisher's function W(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
412. ^
413. ^ 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.
414. ^ Sloane, N. J. A. (ed.). "Sequence A011755". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
415. ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
416. ^ 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.
417. ^ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.