500 (five hundred) is the natural number following 499 and preceding 501.

← 499 500 501 →
Cardinalfive hundred
Ordinal500th
(five hundredth)
Factorization22 × 53
Greek numeralΦ´
Roman numeralD
Binary1111101002
Ternary2001123
Senary21526
Octal7648
Duodecimal35812
Hexadecimal1F416

Mathematical properties edit

500 = 22 × 53. It is an Achilles number and an Harshad number, meaning it is divisible by the sum of its digits. It is the number of planar partitions of 10.[1]

Other fields edit

Five hundred is also

Slang names edit

  • Monkey (UK slang for £500; US slang for $500)[2]

Integers from 501 to 599 edit

500s edit

501 edit

501 = 3 × 167. It is:

  • the sum of the first 18 primes (a term of the sequence OEISA007504).
  • palindromic in bases 9 (6169) and 20 (15120).

502 edit

  • 502 = 2 × 251
  • vertically symmetric number (sequence A053701 in the OEIS)

503 edit

503 is:

504 edit

504 = 23 × 32 × 7. It is:

  is prime[11]

505 edit

506 edit

506 = 2 × 11 × 23. It is:

  is a prime number.

507 edit

  • 507 = 3 × 132 = 232 - 23 + 1, which makes it a central polygonal number[15]
    • The age Ming had before dying.

508 edit

  • 508 = 22 × 127, sum of four consecutive primes (113 + 127 + 131 + 137), number of graphical forest partitions of 30,[16] since 508 = 222 + 22 + 2 it is the maximum number of regions into which 23 intersecting circles divide the plane.[17]

509 edit

509 is:

510s edit

510 edit

510 = 2 × 3 × 5 × 17. It is:

  • the sum of eight consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).
  • the sum of ten consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).
  • the sum of twelve consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).
  • a nontotient.
  • a sparsely totient number.[19]
  • a Harshad number.
  • the number of nonempty proper subsets of an 9-element set.[20]

511 edit

511 = 7 × 73. It is:

512 edit

512 = 83 = 29. It is:

513 edit

513 = 33 × 19. It is:

514 edit

514 = 2 × 257, it is:

515 edit

515 = 5 × 103, it is:

  • the sum of nine consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).
  • the number of complete compositions of 11.[23]

516 edit

516 = 22 × 3 × 43, it is:

517 edit

517 = 11 × 47, it is:

  • the sum of five consecutive primes (97 + 101 + 103 + 107 + 109).
  • a Smith number.[25]

518 edit

518 = 2 × 7 × 37, it is:

  • = 51 + 12 + 83 (a property shared with 175 and 598).
  • a sphenic number.
  • a nontotient.
  • an untouchable number.[24]
  • palindromic and a repdigit in bases 6 (22226) and 36 (EE36).
  • a Harshad number.

519 edit

519 = 3 × 173, it is:

  • the sum of three consecutive primes (167 + 173 + 179)
  • palindromic in bases 9 (6369) and 12 (37312)
  • a D-number.[26]

520s edit

520 edit

520 = 23 × 5 × 13. It is:

521 edit

521 is:

  • a Lucas prime.[27]
  • A Mersenne exponent, i.e. 2521−1 is prime.
  • a Chen prime.
  • an Eisenstein prime with no imaginary part.
  • palindromic in bases 11 (43411) and 20 (16120).

4521 - 3521 is prime

522 edit

522 = 2 × 32 × 29. It is:

  • the sum of six consecutive primes (73 + 79 + 83 + 89 + 97 + 101).
  • a repdigit in bases 28 (II28) and 57 (9957).
  • a Harshad number.
  • number of series-parallel networks with 8 unlabeled edges.[29]

523 edit

523 is:

  • a prime number.
  • the sum of seven consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89).
  • palindromic in bases 13 (31313) and 18 (1B118).
  • a prime with a prime number of prime digits[30]
  • the smallest prime number that starts a prime gap of length greater than 14

524 edit

524 = 22 × 131

  • number of partitions of 44 into powers of 2[31]

525 edit

525 = 3 × 52 × 7. It is palindromic in base ten, as well as the fifty-fifth self number greater than 1 in decimal.[32] It is also:

525 is the number of scan lines in the NTSC television standard.

526 edit

526 = 2 × 263, centered pentagonal number,[35] nontotient, Smith number[25]

527 edit

527 = 17 × 31. it is:

  • palindromic in base 15 (25215)
  • number of diagonals in a 34-gon[36]
  • also, the section of the US Tax Code regulating soft money political campaigning (see 527 groups)

528 edit

528 = 24 × 3 × 11. It is:

529 edit

529 = 232. It is:

530s edit

530 edit

530 = 2 × 5 × 53. It is:

531 edit

531 = 32 × 59. It is:

  • palindromic in base 12 (38312).
  • a Harshad number.
  • number of symmetric matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to 6[38]

532 edit

532 = 22 × 7 × 19. It is:

533 edit

533 = 13 × 41. It is:

  • the sum of three consecutive primes (173 + 179 + 181).
  • the sum of five consecutive primes (101 + 103 + 107 + 109 + 113).
  • palindromic in base 19 (19119).
  • generalized octagonal number.[40]

534 edit

534 = 2 × 3 × 89. It is:

  • a sphenic number.
  • the sum of four consecutive primes (127 + 131 + 137 + 139).
  • a nontotient.
  • palindromic in bases 5 (41145) and 14 (2A214).
  • an admirable number.
  is prime[11]

535 edit

535 = 5 × 107. It is:

  for  ; this polynomial plays an essential role in Apéry's proof that   is irrational.

535 is used as an abbreviation for May 35, which is used in China instead of June 4 to evade censorship by the Chinese government of references on the Internet to the Tiananmen Square protests of 1989.[41]

536 edit

536 = 23 × 67. It is:

  • the number of ways to arrange the pieces of the ostomachion into a square, not counting rotation or reflection.
  • the number of 1's in all partitions of 23 into odd parts[42]
  • a refactorable number.[10]
  • the lowest happy number beginning with the digit 5.

537 edit

537 = 3 × 179, Mertens function (537) = 0, Blum integer, D-number[26]

538 edit

538 = 2 × 269. It is:

539 edit

539 = 72 × 11

  is prime[11]

540s edit

540 edit

540 = 22 × 33 × 5. It is:

541 edit

541 is:

For the Mertens function,  

542 edit

542 = 2 × 271. It is:

543 edit

543 = 3 × 181; palindromic in bases 11 (45411) and 12 (39312), D-number.[26]

  is prime[11]

544 edit

544 = 25 × 17. Take a grid of 2 times 5 points. There are 14 points on the perimeter. Join every pair of the perimeter points by a line segment. The lines do not extend outside the grid. 544 is the number of regions formed by these lines. OEISA331452

544 is also the number of pieces that could be seen in a 5×5×5×5 Rubik's Tesseract. As a standard 5×5×5 has 98 visible pieces (53 − 33), a 5×5×5×5 has 544 visible pieces (54 − 34).

545 edit

545 = 5 × 109. It is:

546 edit

546 = 2 × 3 × 7 × 13. It is:

  • the sum of eight consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).
  • palindromic in bases 4 (202024), 9 (6669), and 16 (22216).
  • a repdigit in bases 9 and 16.
  • 546! − 1 is prime.

547 edit

547 is:

548 edit

548 = 22 × 137. It is:

Also, every positive integer is the sum of at most 548 ninth powers;

549 edit

549 = 32 × 61, it is:

  • a repdigit in bases 13 (33313) and 60 (9960).
  • φ(549) = φ(σ(549)).[55]

550s edit

550 edit

550 = 2 × 52 × 11. It is:

551 edit

551 = 19 × 29. It is:

  • It is the number of mathematical trees on 12 unlabeled nodes.[58]
  • the sum of three consecutive primes (179 + 181 + 191).
  • palindromic in base 22 (13122).
  • the SMTP status code meaning user is not local

552 edit

552 = 23 × 3 × 23. It is:

  • the sum of six consecutive primes (79 + 83 + 89 + 97 + 101 + 103).
  • the sum of ten consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).
  • a pronic number.[14]
  • an untouchable number.[24]
  • palindromic in base 19 (1A119).
  • a Harshad number.
  • the model number of U-552.
  • the SMTP status code meaning requested action aborted because the mailbox is full.

553 edit

553 = 7 × 79. It is:

  • the sum of nine consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).
  • central polygonal number.[15]
  • the model number of U-553.
  • the SMTP status code meaning requested action aborted because of faulty mailbox name.

554 edit

554 = 2 × 277. It is:

  • a nontotient.
  • a 2-Knödel number
  • the SMTP status code meaning transaction failed.

Mertens function(554) = 6, a record high that stands until 586.

555 edit

555 = 3 × 5 × 37 is:

  • a sphenic number.
  • palindromic in bases 9 (6769), 10 (55510), and 12 (3A312).
  • a repdigit in bases 10 and 36.
  • a Harshad number.
  • φ(555) = φ(σ(555)).[55]

556 edit

556 = 22 × 139. It is:

  • the sum of four consecutive primes (131 + 137 + 139 + 149).
  • an untouchable number, because it is never the sum of the proper divisors of any integer.[24]
  • a happy number.
  • the model number of U-556; 5.56×45mm NATO cartridge.

557 edit

557 is:

  • a prime number.
  • a Chen prime.
  • an Eisenstein prime with no imaginary part.
  • the number of parallelogram polyominoes with 9 cells.[59]

558 edit

558 = 2 × 32 × 31. It is:

  • a nontotient.
  • a repdigit in bases 30 (II30) and 61 (9961).
  • a Harshad number.
  • The sum of the largest prime factors of the first 558 is itself divisible by 558 (the previous such number is 62, the next is 993).
  • in the title of the Star Trek: Deep Space Nine episode "The Siege of AR-558"

559 edit

559 = 13 × 43. It is:

  • the sum of five consecutive primes (103 + 107 + 109 + 113 + 127).
  • the sum of seven consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97).
  • a nonagonal number.[60]
  • a centered cube number.[61]
  • palindromic in base 18 (1D118).
  • the model number of U-559.

560s edit

560 edit

560 = 24 × 5 × 7. It is:

  • a tetrahedral number.[62]
  • a refactorable number.
  • palindromic in bases 3 (2022023) and 6 (23326).
  • the number of diagonals in a 35-gon[36]

561 edit

561 = 3 × 11 × 17. It is:

562 edit

562 = 2 × 281. It is:

  • a Smith number.[25]
  • an untouchable number.[24]
  • the sum of twelve consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).
  • palindromic in bases 4 (203024), 13 (34313), 14 (2C214), 16 (23216), and 17 (1G117).
  • a lazy caterer number (sequence A000124 in the OEIS).
  • the number of Native American (including Alaskan) Nations, or "Tribes," recognized by the USA government.

56264 + 1 is prime

563 edit

563 is:

564 edit

564 = 22 × 3 × 47. It is:

  • the sum of a twin prime (281 + 283).
  • a refactorable number.
  • palindromic in bases 5 (42245) and 9 (6869).
  • number of primes <= 212.[69]

565 edit

565 = 5 × 113. It is:

  • the sum of three consecutive primes (181 + 191 + 193).
  • a member of the Mian–Chowla sequence.[70]
  • a happy number.
  • palindromic in bases 10 (56510) and 11 (47411).

566 edit

566 = 2 × 283. It is:

567 edit

567 = 34 × 7. It is:

  • palindromic in base 12 (3B312).
  is prime[11]

568 edit

568 = 23 × 71. It is:

  • the sum of the first nineteen primes (a term of the sequence OEISA007504).
  • a refactorable number.
  • palindromic in bases 7 (14417) and 21 (16121).
  • the smallest number whose seventh power is the sum of 7 seventh powers.
  • the room number booked by Benjamin Braddock in the 1967 film The Graduate.
  • the number of millilitres in an imperial pint.
  • the name of the Student Union bar at Imperial College London

569 edit

569 is:

  • a prime number.
  • a Chen prime.
  • an Eisenstein prime with no imaginary part.
  • a strictly non-palindromic number.[67]

570s edit

570 edit

570 = 2 × 3 × 5 × 19. It is:

  • a triangular matchstick number[71]
  • a balanced number[72]

571 edit

571 is:

  • a prime number.
  • a Chen prime.
  • a centered triangular number.[22]
  • the model number of U-571 which appeared in the 2000 movie U-571

572 edit

572 = 22 × 11 × 13. It is:

573 edit

573 = 3 × 191. It is:

574 edit

574 = 2 × 7 × 41. It is:

  • a sphenic number.
  • a nontotient.
  • palindromic in base 9 (7079).
  • number of partitions of 27 that do not contain 1 as a part.[73]

575 edit

575 = 52 × 23. It is:

And the sum of the squares of the first 575 primes is divisible by 575.[75]

576 edit

576 = 26 × 32 = 242. It is:

  • the sum of four consecutive primes (137 + 139 + 149 + 151).
  • a highly totient number.[76]
  • a Smith number.[25]
  • an untouchable number.[24]
  • palindromic in bases 11 (48411), 14 (2D214), and 23 (12123).
  • a Harshad number.
  • four-dozen sets of a dozen, which makes it 4 gross.
  • a cake number.
  • the number of parts in all compositions of 8.[77]

577 edit

577 is:

578 edit

578 = 2 × 172. It is:

  • a nontotient.
  • palindromic in base 16 (24216).
  • area of a square with diagonal 34[79]

579 edit

579 = 3 × 193; it is a ménage number,[80] and a semiprime.

580s edit

580 edit

580 = 22 × 5 × 29. It is:

  • the sum of six consecutive primes (83 + 89 + 97 + 101 + 103 + 107).
  • palindromic in bases 12 (40412) and 17 (20217).

581 edit

581 = 7 × 83. It is:

  • the sum of three consecutive primes (191 + 193 + 197).
  • a Blum integer

582 edit

582 = 2 × 3 × 97. It is:

  • a sphenic number.
  • the sum of eight consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89).
  • a nontotient.
  • a vertically symmetric number (sequence A053701 in the OEIS).
  • an admirable number.

583 edit

583 = 11 × 53. It is:

  • palindromic in base 9 (7179).
  • number of compositions of 11 whose run-lengths are either weakly increasing or weakly decreasing[81]

584 edit

584 = 23 × 73. It is:

  • an untouchable number.[24]
  • the sum of totient function for first 43 integers.
  • a refactorable number.

585 edit

585 = 32 × 5 × 13. It is:

  • palindromic in bases 2 (10010010012), 8 (11118), and 10 (58510).
  • a repdigit in bases 8, 38, 44, and 64.
  • the sum of powers of 8 from 0 to 3.

When counting in binary with fingers, expressing 585 as 1001001001, results in the isolation of the index and little fingers of each hand, "throwing up the horns".

586 edit

586 = 2 × 293.

587 edit

587 is:

  • a prime number.
  • safe prime.[3]
  • a Chen prime.
  • an Eisenstein prime with no imaginary part.
  • the sum of five consecutive primes (107 + 109 + 113 + 127 + 131).
  • palindromic in bases 11 (49411) and 15 (29215).
  • the outgoing port for email message submission.
  • a prime index prime.

588 edit

588 = 22 × 3 × 72. It is:

  • a Smith number.[25]
  • palindromic in base 13 (36313).
  • a Harshad number.

589 edit

589 = 19 × 31. It is:

590s edit

590 edit

590 = 2 × 5 × 59. It is:

591 edit

591 = 3 × 197, D-number[26]

592 edit

592 = 24 × 37. It is:

  • palindromic in bases 9 (7279) and 12 (41412).
  • a Harshad number.

59264 + 1 is prime

593 edit

593 is:

  • a prime number.
  • a Sophie Germain prime.
  • the sum of seven consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101).
  • the sum of nine consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).
  • an Eisenstein prime with no imaginary part.
  • a balanced prime.[66]
  • a Leyland prime.
  • a member of the Mian–Chowla sequence.[70]
  • strictly non-palindromic prime.[67]

594 edit

594 = 2 × 33 × 11. It is:

  • the sum of ten consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).
  • a nontotient.
  • palindromic in bases 5 (43345) and 16 (25216).
  • a Harshad number.
  • the number of diagonals in a 36-gon.[36]
  • a balanced number.[72]

595 edit

595 = 5 × 7 × 17. It is:

596 edit

596 = 22 × 149. It is:

  • the sum of four consecutive primes (139 + 149 + 151 + 157).
  • a nontotient.
  • a lazy caterer number (sequence A000124 in the OEIS).

597 edit

597 = 3 × 199. It is:

598 edit

598 = 2 × 13 × 23 = 51 + 92 + 83. It is:

599 edit

599 is:

  • a prime number.
  • a Chen prime.
  • an Eisenstein prime with no imaginary part.
  • a prime index prime.

4599 - 3599 is prime.

References edit

  1. ^ 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.
  2. ^ Evans, I.H., Brewer's Dictionary of Phrase and Fable, 14th ed., Cassell, 1990, ISBN 0-304-34004-9
  3. ^ a b c Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  4. ^ that is, a term of the sequence OEISA034961
  5. ^ that is, the first term of the sequence OEISA133525
  6. ^ since 503+2 is a product of two primes, 5 and 101
  7. ^ since it is a prime which is congruent to 2 modulo 3.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A001606 (Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A000073 (Tribonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  10. ^ a b c Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  11. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  12. ^ Wohlfahrt, K. (1985). "Macbeath's curve and the modular group". Glasgow Math. J. 27: 239–247. doi:10.1017/S0017089500006212. MR 0819842.
  13. ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  14. ^ a b Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  15. ^ a b Sloane, N. J. A. (ed.). "Sequence A002061". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ^ Sloane, N. J. A. (ed.). "Sequence A000070". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A014206". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ^ Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  19. ^ Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  20. ^ Sloane, N. J. A. (ed.). "Sequence A000918". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^ Sloane, N. J. A. (ed.). "Sequence A061209 (Numbers which are the cubes of their digit sum)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  22. ^ a b Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  23. ^ Sloane, N. J. A. (ed.). "Sequence A107429 (Number of complete compositions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  24. ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A005114 (Untouchable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  25. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  26. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A033553 (3-Knödel numbers or D-numbers: numbers n > 3 such that n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
  27. ^ Sloane, N. J. A. (ed.). "Sequence A005479 (Prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  28. ^ Dr. Kirkby (May 19, 2021). "Many more twin primes below Mersenne exponents than above Mersenne exponents". Mersenne Forum.
  29. ^ 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.
  30. ^ Sloane, N. J. A. (ed.). "Sequence A348699 (Primes with a prime number of prime digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  31. ^ Sloane, N. J. A. (ed.). "Sequence A000123 (Number of binary partitions: number of partitions of 2n into powers of 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  32. ^ Sloane, N. J. A. (ed.). "Sequence A003052 (Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-09.
  33. ^ Sloane, N. J. A. (ed.). "Sequence A329191 (The prime divisors of the orders of the sporadic finite simple groups.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-09.
  34. ^ Sloane, N. J. A. (ed.). "Sequence A113907 (Dimensions of the five sporadic Lie groups.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-09.
  35. ^ Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  36. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000096". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
  37. ^ Sloane, N. J. A. (ed.). "Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  38. ^ Sloane, N. J. A. (ed.). "Sequence A138178 (Number of symmetric matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  39. ^ a b Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  40. ^ Sloane, N. J. A. (ed.). "Sequence A001082 (Generalized octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  41. ^ Larmer, Brook (October 26, 2011). "Where an Internet Joke Is Not Just a Joke". New York Times. Retrieved November 1, 2011.
  42. ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  43. ^ Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  44. ^ Snorri Sturluson (1880). "Prose Edda". p. 107.
  45. ^ Snorri Sturluson (1880). "Prose Edda". p. 82.
  46. ^ Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  47. ^ Sloane, N. J. A. (ed.). "Sequence A003154 (Centered 12-gonal numbers. Also star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  48. ^ Sloane, N. J. A. (ed.). "Sequence A000670 (Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n].)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-10-23.
  49. ^ Sloane, N. J. A. (ed.). "Sequence A059801 (Numbers k such that 4^k - 3^k is prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-10-23.
  50. ^ Sloane, N. J. A. (ed.). "Sequence A002088". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  51. ^ Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  52. ^ Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  53. ^ Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  54. ^ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  55. ^ a b Sloane, N. J. A. (ed.). "Sequence A006872". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  56. ^ Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  57. ^ a b Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  58. ^ "Sloane's A000055: Number of trees with n unlabeled nodes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2010-11-29. Retrieved 2021-12-19.
  59. ^ 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.
  60. ^ Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  61. ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  62. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  63. ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  64. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 14. ISBN 978-1-84800-000-1.
  65. ^ Sloane, N. J. A. (ed.). "Sequence A007540 (Wilson primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  66. ^ a b Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  67. ^ a b c Sloane, N. J. A. (ed.). "Sequence A016038 (Strictly non-palindromic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  68. ^ 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.
  69. ^ Sloane, N. J. A. (ed.). "Sequence A007053". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  70. ^ a b Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  71. ^ Sloane, N. J. A. (ed.). "Sequence A045943". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  72. ^ a b Sloane, N. J. A. (ed.). "Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  73. ^ 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.
  74. ^ 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.
  75. ^ Sloane, N. J. A. (ed.). "Sequence A111441 (Numbers k such that the sum of the squares of the first k primes is divisible by k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  76. ^ Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  77. ^ Sloane, N. J. A. (ed.). "Sequence A001792". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  78. ^ Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  79. ^ Sloane, N. J. A. (ed.). "Sequence A001105". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  80. ^ Sloane, N. J. A. (ed.). "Sequence A000179 (Ménage numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  81. ^ 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.
  82. ^ Sloane, N. J. A. (ed.). "Sequence A060544 (Centered 9-gonal (also known as nonagonal or enneagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.