500 (number)
This article needs additional citations for verification. (January 2019) |
| ||||
---|---|---|---|---|
Cardinal | five hundred | |||
Ordinal | 500th (five hundredth) | |||
Factorization | 22 × 53 | |||
Greek numeral | Φ´ | |||
Roman numeral | D | |||
Binary | 1111101002 | |||
Ternary | 2001123 | |||
Senary | 21526 | |||
Octal | 7648 | |||
Duodecimal | 35812 | |||
Hexadecimal | 1F416 | |||
Armenian | Շ | |||
Hebrew | ת"ק / ך | |||
Babylonian cuneiform | 𒐜⟪ | |||
Egyptian hieroglyph | 𓍦 |
500 (five hundred) is the natural number following 499 and preceding 501.
Mathematical properties
[edit]500 = 22 × 53. It is an Achilles number and a 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
- the number that many NASCAR races often use at the end of their race names (e.g., Daytona 500), to denote the length of the race (in miles, kilometers or laps).
- the longest advertised distance (in miles) of the IndyCar Series and its premier race, the Indianapolis 500.
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 OEIS: A007504).
- palindromic in bases 9 (6169) and 20 (15120).
502
[edit]503
[edit]503 is:
- a prime number.
- a safe prime.[3]
- the sum of three consecutive primes (163 + 167 + 173).[4]
- the sum of the cubes of the first four primes.[5]
- a Chen prime[6]
- an Eisenstein prime with no imaginary part.[7]
- an index of a prime Lucas number.[8]
- an isolated prime
504
[edit]504 = 23 × 32 × 7. It is:
- the sum between the smallest pair of amicable numbers (220, 284).[9]
- a tribonacci number.[10]
- a semi-meandric number.
- a refactorable number.[11]
- a Harshad number.
- is prime[12]
- the group order of the fourth smallest non-cyclic simple group A1(8) = 2G2(3)′.
- the number of symmetries of the simple group PSL(2,8) that is the automorphism group of the Macbeath surface.[13]
- a largely composite number[14]
505
[edit]- 505 = 5 × 101
- model number of Levi's jeans, model number of U-505
- This number is the magic constant of n×n normal magic square and n-queens problem for n = 10.
506
[edit]506 = 2 × 11 × 23. It is:
- a sphenic number.
- a square pyramidal number.[15]
- a pronic number.[16]
- a Harshad number.
is a prime number. Its decimal expansion is 252 nines, an eight, and 253 more nines.
507
[edit]- 507 = 3 × 132 = 232 - 23 + 1, which makes it a central polygonal number[17]
- 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,[18] since 508 = 222 + 22 + 2 it is the maximum number of regions into which 23 intersecting circles divide the plane.[19]
509
[edit]509 is:
- a prime number.
- a Sophie Germain prime, smallest Sophie Germain prime to start a 4-term Cunningham chain of the first kind {509, 1019, 2039, 4079}.
- a Chen prime.
- an Eisenstein prime with no imaginary part.
- a highly cototient number[20]
- a prime index prime.
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.[21]
- a Harshad number.
- the number of nonempty proper subsets of an 9-element set.[22]
511
[edit]511 = 7 × 73. It is:
- a Harshad number.
- a palindromic number and a repdigit in bases 2 (1111111112) and 8 (7778)
- 5-1-1, a roadway status and transit information hotline in many metropolitan areas of the United States.
512
[edit]512 = 83 = 29. It is:
- a power of two.
- a cube of 8.
- a Leyland number.
- a Dudeney number.[23]
- a Harshad number.
- palindromic in bases 7 (13317) and 15 (24215).
- a vertically symmetric number (sequence A053701 in the OEIS).
513
[edit]513 = 33 × 19. It is:
- Leyland number of the second kind
- palindromic in bases 2 (10000000012) and 8 (10018)
- a Harshad number
- Area code of Cincinnati, Ohio
514
[edit]514 = 2 × 257, it is:
- a centered triangular number.[24]
- a nontotient
- a palindrome in bases 4 (200024), 16 (20216), and 19 (18119)
- an Area Code for Montreal, Canada
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.[25]
516
[edit]516 = 22 × 3 × 43, it is:
- nontotient.
- untouchable number.[26]
- refactorable number.[11]
- a Harshad number.
517
[edit]517 = 11 × 47, it is:
- the sum of five consecutive primes (97 + 101 + 103 + 107 + 109).
- a Smith number.[27]
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.[26]
- 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.[28]
520s
[edit]520
[edit]520 = 23 × 5 × 13. It is:
- an untouchable number.[26]
- an idoneal number
- a palindromic number in base 14 (29214).
521
[edit]521 is:
- a Lucas prime.[29]
- A Mersenne exponent, i.e. 2521−1 is prime.
- The largest known such exponent that is the lesser of twin primes[30]
- a Chen prime.
- an Eisenstein prime with no imaginary part.
- palindromic in bases 11 (43411) and 20 (16120).
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.[31]
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[32]
- 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[33]
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.[34] It is also:
- the sum of all prime numbers that divide the orders of the twenty-six sporadic groups (2, 3, 5, ..., 71; aside from 53 and 61).[35]
- the sum of the dimensions of all five exceptional Lie algebras (14, 52, 78, 133, 248).[36]
525 is the number of scan lines in the NTSC television standard.
526
[edit]526 = 2 × 263, centered pentagonal number,[37] nontotient, Smith number[27]
527
[edit]527 = 17 × 31. It is:
- palindromic in base 15 (25215)
- number of diagonals in a 34-gon[38]
- also, the section of the US Tax Code regulating soft money political campaigning (see 527 groups)
528
[edit]528 = 24 × 3 × 11. It is:
- a triangular number.
- palindromic in bases 9 (6469) and 17 (1E117).
529
[edit]529 = 232. It is:
- a centered octagonal number.[39]
- a lazy caterer number (sequence A000124 in the OEIS).
- also Section 529 of the IRS tax code organizes 529 plans to encourage saving for higher education.
530s
[edit]530
[edit]530 = 2 × 5 × 53. It is:
- a sphenic number.
- a nontotient.
- the sum of totient function for first 41 integers.
- an untouchable number.[26]
- the sum of the first three perfect numbers.
- palindromic in bases 4 (201024), 16 (21216), and 23 (10123).
- a US telephone area code that covers much of Northern California.
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[40]
532
[edit]532 = 22 × 7 × 19. It is:
- a pentagonal number.[41]
- a nontotient.
- palindromic and a repdigit in bases 11 (44411), 27 (JJ27), and 37 (EE37).
- admirable number.
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.[42]
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[12]
535
[edit]535 = 5 × 107. It is:
- a Smith number.[27]
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.[43]
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[44]
- a refactorable number.[11]
- the lowest happy number beginning with the digit 5.
537
[edit]537 = 3 × 179, Mertens function (537) = 0, Blum integer, D-number[28]
538
[edit]538 = 2 × 269. It is:
- an open meandric number.
- a nontotient.
- the total number of votes in the United States Electoral College.
- the website FiveThirtyEight.
- Radio 538, a Dutch commercial radio station
539
[edit]539 = 72 × 11
is prime[12]
540s
[edit]540
[edit]540 = 22 × 33 × 5. It is:
- an untouchable number.[26]
- a heptagonal number.
- a decagonal number.[45]
- a repdigit in bases 26 (KK26), 29 (II29), 35 (FF35), 44 (CC44), 53 (AA53), and 59 (9959).
- a Harshad number.
- the number of doors to Valhalla according to the Prose Edda.[46]
- the number of floors in Thor's hall, known as Bilskirnir, according to the Prose Edda.[47]
- the sum of a twin prime (269 + 271)
- a largely composite number[14]
541
[edit]541 is:
- the 100th prime.
- a lucky prime.[48]
- a Chen prime.
- the 10th star number.[49]
- palindromic in bases 18 (1C118) and 20 (17120).
- the fifth ordered Bell number that represents the number of ordered partitions of .[50]
- 4541 - 3541 is prime.[51]
For the Mertens function,
542
[edit]542 = 2 × 271. It is:
- a nontotient.
- the sum of totient function for the first 42 integers.[52]
543
[edit]543 = 3 × 181; palindromic in bases 11 (45411) and 12 (39312), D-number.[28]
is prime[12]
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. OEIS: A331452
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:
- a centered square number.[53]
- palindromic in bases 10 (54510) and 17 (1F117).
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:
- a prime number.
- a cuban prime.[54]
- a centered hexagonal number.[55]
- a centered heptagonal number.[56]
- a prime index prime.
548
[edit]548 = 22 × 137. It is:
- a nontotient.
- the default port for the Apple Filing Protocol.
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)).[57]
550s
[edit]550
[edit]550 = 2 × 52 × 11. It is:
- a pentagonal pyramidal number.[58]
- a primitive abundant number.[59]
- a nontotient.
- a repdigit in bases 24 (MM24), 49 (BB49), and 54 (AA54).
- a Harshad number.
- the SMTP status code meaning the requested action was not taken because the mailbox is unavailable
551
[edit]551 = 19 × 29. It is:
- It is the number of mathematical trees on 12 unlabeled nodes.[60]
- 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 number of prime knots with 11 crossings.[61]
- 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.[16]
- an untouchable number.[26]
- 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.[17]
- 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)).[57]
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.[26]
- 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.[62]
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.[63]
- a centered cube number.[64]
- palindromic in base 18 (1D118).
- the model number of U-559.
560s
[edit]560
[edit]560 = 24 × 5 × 7. It is:
- a tetrahedral number.[65]
- a refactorable number.
- palindromic in bases 3 (2022023) and 6 (23326).
- the number of diagonals in a 35-gon[38]
561
[edit]561 = 3 × 11 × 17. It is:
- a sphenic number.
- a triangular number.
- a hexagonal number.[66]
- palindromic in bases 2 (10001100012) and 20 (18120).
- the first Carmichael number[67]
562
[edit]562 = 2 × 281. It is:
- a Smith number.[27]
- an untouchable number.[26]
- 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.
563
[edit]563 is:
- a prime number.
- a safe prime.[3]
- the largest known Wilson prime.[68]
- a Chen prime.
- an Eisenstein prime with no imaginary part.
- a balanced prime.[69]
- a strictly non-palindromic number.[70]
- a sexy prime.
- a happy prime.
- a prime index prime.
- 5563 - 4563 is prime.[71]
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.[72]
565
[edit]565 = 5 × 113. It is:
- the sum of three consecutive primes (181 + 191 + 193).
- a member of the Mian–Chowla sequence.[73]
- a happy number.
- palindromic in bases 10 (56510) and 11 (47411).
566
[edit]566 = 2 × 283. It is:
- nontotient.
- a happy number.
- a 2-Knödel number.
567
[edit]567 = 34 × 7. It is:
- palindromic in base 12 (3B312).
- is prime[12]
568
[edit]568 = 23 × 71. It is:
- the sum of the first nineteen primes (a term of the sequence OEIS: A007504).
- 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.[70]
570s
[edit]570
[edit]570 = 2 × 3 × 5 × 19. It is:
571
[edit]571 is:
- a prime number.
- a Chen prime.
- a centered triangular number.[24]
- the model number of U-571 which appeared in the 2000 movie U-571
572
[edit]572 = 22 × 11 × 13. It is:
- a primitive abundant number.[59]
- a nontotient.
- palindromic in bases 3 (2100123) and 15 (28215).
573
[edit]573 = 3 × 191. It is:
- a Blum integer
- known as the Konami number, since "ko-na-mi" is associated with 573 in the Japanese wordplay Goroawase
- the model number of German submarine U-573
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.[76]
- number of amino acid residues in a hemoglobin molecule.
575
[edit]575 = 52 × 23. It is:
- palindromic in bases 10 (57510) and 13 (35313).
- a centered octahedral number.[77]
And the sum of the squares of the first 575 primes is divisible by 575.[78]
576
[edit]576 = 26 × 32 = 242. It is:
- the sum of four consecutive primes (137 + 139 + 149 + 151).
- a highly totient number.[79]
- a Smith number.[27]
- an untouchable number.[26]
- 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.[80]
577
[edit]577 is:
- a prime number.
- a Proth prime.[81]
- a Chen prime.
- palindromic in bases 18 (1E118) and 24 (10124).
- the number of seats in National Assembly (France).
578
[edit]578 = 2 × 172. It is:
- a nontotient.
- palindromic in base 16 (24216).
- area of a square with diagonal 34[82]
579
[edit]579 = 3 × 193; it is a ménage number,[83] 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[84]
584
[edit]584 = 23 × 73. It is:
- an untouchable number.[26]
- 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.
- Mertens function(586) = 7 a record high that stands until 1357.
- 2-Knödel number.
- it is the number of several popular personal computer processors (such as the Intel Pentium).
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.[27]
- palindromic in base 13 (36313).
- a Harshad number.
589
[edit]589 = 19 × 31. It is:
- the sum of three consecutive primes (193 + 197 + 199).
- palindromic in base 21 (17121).
- a centered tetrahedral number.
590s
[edit]590
[edit]590 = 2 × 5 × 59. It is:
- a sphenic number.
- a pentagonal number.[41]
- a nontotient.
- palindromic in base 19 (1C119).
591
[edit]592
[edit]592 = 24 × 37. It is:
- palindromic in bases 9 (7279) and 12 (41412).
- a Harshad number.
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.[69]
- a Leyland prime.
- a member of the Mian–Chowla sequence.[73]
- a strictly non-palindromic number.[70]
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.[38]
- a balanced number.[75]
595
[edit]595 = 5 × 7 × 17. It is:
- a sphenic number.
- a triangular number.
- centered nonagonal number.[85]
- palindromic in bases 10 (59510) and 18 (1F118).
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:
- a sphenic number.
- palindromic in bases 4 (211124) and 11 (4A411).
- number of non-alternating permutations of {1...6}.
599
[edit]599 is:
- a prime number.
- a Chen prime.
- an Eisenstein prime with no imaginary part.
- a prime index prime.
References
[edit]- ^ 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.
- ^ Evans, I.H., Brewer's Dictionary of Phrase and Fable, 14th ed., Cassell, 1990, ISBN 0-304-34004-9
- ^ 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.
- ^ that is, a term of the sequence OEIS: A034961
- ^ that is, the first term of the sequence OEIS: A133525
- ^ since 503+2 is a product of two primes, 5 and 101
- ^ since it is a prime which is congruent to 2 modulo 3.
- ^ Sloane, N. J. A. (ed.). "Sequence A001606 (Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A259180 (Amicable pairs.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-05-22.
- ^ Sloane, N. J. A. (ed.). "Sequence A000073 (Tribonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ 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.
- ^ 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.
- ^ Wohlfahrt, K. (1985). "Macbeath's curve and the modular group". Glasgow Math. J. 27: 239–247. doi:10.1017/S0017089500006212. MR 0819842.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ 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.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A002061". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000070". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A000918". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A107429 (Number of complete compositions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A005479 (Prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Dr. Kirkby (May 19, 2021). "Many more twin primes below Mersenne exponents than above Mersenne exponents". Mersenne Forum.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A348699 (Primes with a prime number of prime digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A000096". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ 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.
- ^ 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.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A001082 (Generalized octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Larmer, Brook (October 26, 2011). "Where an Internet Joke Is Not Just a Joke". New York Times. Retrieved November 1, 2011.
- ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ Snorri Sturluson (1880). "Prose Edda". p. 107.
- ^ Snorri Sturluson (1880). "Prose Edda". p. 82.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A002088". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A006872". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ 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.
- ^ "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.
- ^ Sloane, N. J. A. (ed.). "Sequence A002863 (Number of prime knots with n crossings)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 14. ISBN 978-1-84800-000-1.
- ^ Sloane, N. J. A. (ed.). "Sequence A007540 (Wilson primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ 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.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A007053". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A045943". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A001792". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A001105". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000179 (Ménage numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ 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.
- ^ 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.