600 (number)
(Redirected from 690 (number))
| ||||
|---|---|---|---|---|
| Cardinal | six hundred | |||
| Ordinal | 600th (six hundredth) | |||
| Factorization | 23 × 3 × 52 | |||
| Divisors | 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600 | |||
| Greek numeral | Χ´ | |||
| Roman numeral | DC | |||
| Binary | 10010110002 | |||
| Ternary | 2110203 | |||
| Senary | 24406 | |||
| Octal | 11308 | |||
| Duodecimal | 42012 | |||
| Hexadecimal | 25816 | |||
| Armenian | Ո | |||
| Hebrew | ת"ר / ם | |||
| Babylonian cuneiform | 𒌋 | |||
| Egyptian hieroglyph | 𓍧 | |||
600 (six hundred) is the natural number following 599 and preceding 601.
Mathematical properties
[edit]Six hundred is a composite number, an abundant number, a pronic number,[1] a Harshad number and a largely composite number.[2]
Credit and cars
[edit]- In the United States, a credit score of 600 or below is considered poor, limiting available credit at a normal interest rate
- NASCAR runs 600 advertised miles in the Coca-Cola 600, its longest race
- The Fiat 600 is a car, the SEAT 600 its Spanish version
Integers from 601 to 699
[edit]600s
[edit]- 601 = prime number, centered pentagonal number[3]
- 602 = 2 × 7 × 43, nontotient, number of cubes of edge length 1 required to make a hollow cube of edge length 11, area code for Phoenix, AZ along with 480 and 623
- 603 = 32 × 67, Harshad number, Riordan number, area code for New Hampshire
- 604 = 22 × 151, nontotient, totient sum for first 44 integers, area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky)
- 605 = 5 × 112, Harshad number, sum of the nontriangular numbers between the two successive triangular numbers 55 and 66, number of non-isomorphic set-systems of weight 9
- 606 = 2 × 3 × 101, sphenic number, sum of six consecutive primes (89 + 97 + 101 + 103 + 107 + 109), admirable number, One of the numbers associated with Christ - ΧϚʹ - see the Greek numerals Isopsephy and the reason why other numbers siblings with this one are Beast's numbers.
- 607 – prime number, sum of three consecutive primes (197 + 199 + 211), Mertens function(607) = 0, balanced prime,[4] strictly non-palindromic number,[5] Mersenne prime exponent
- 608 = 25 × 19, Mertens function(608) = 0, nontotient, happy number, number of regions formed by drawing the line segments connecting any two of the perimeter points of a 3 times 4 grid of squares[6]
- 609 = 3 × 7 × 29, sphenic number, strobogrammatic number[7]
610s
[edit]- 610 = 2 × 5 × 61, sphenic number, Fibonacci number,[8] Markov number,[9] also a kind of telephone wall socket used in Australia
- 611 = 13 × 47, sum of the three standard board sizes in Go (92 + 132 + 192), the 611th tribonacci number is prime
- 612 = 22 × 32 × 17, Harshad number, Zuckerman number (sequence A007602 in the OEIS), untouchable number, area code for Minneapolis, MN
- 613 = prime number, first number of prime triple (p, p + 4, p + 6), middle number of sexy prime triple (p − 6, p, p + 6). Geometrical numbers: Centered square number with 18 per side, circular number of 21 with a square grid and 27 using a triangular grid. Also 17-gonal. Hypotenuse of a right triangle with integral sides, these being 35 and 612. Partitioning: 613 partitions of 47 into non-factor primes, 613 non-squashing partitions into distinct parts of the number 54. Squares: Sum of squares of two consecutive integers, 17 and 18. Additional properties: a lucky number, index of prime Lucas number.[10]
- In Judaism the number 613 is very significant, as its metaphysics, the Kabbalah, views every complete entity as divisible into 613 parts: 613 parts of every Sefirah; 613 mitzvot, or divine Commandments in the Torah; 613 parts of the human body.
- The number 613 hangs from the rafters at Madison Square Garden in honor of New York Knicks coach Red Holzman's 613 victories
- 614 = 2 × 307, nontotient, 2-Knödel number. According to Rabbi Emil Fackenheim, the number of Commandments in Judaism should be 614 rather than the traditional 613.
- 615 = 3 × 5 × 41, sphenic number
- 616 = 23 × 7 × 11, Padovan number, balanced number,[11] an alternative value for the Number of the Beast (more commonly accepted to be 666)
- 617 = prime number, sum of five consecutive primes (109 + 113 + 127 + 131 + 137), Chen prime, Eisenstein prime with no imaginary part, number of compositions of 17 into distinct parts,[12] prime index prime, index of prime Lucas number[10]
- Area code 617, a telephone area code covering the metropolitan Boston area
- 618 = 2 × 3 × 103, sphenic number, admirable number
- 619 = prime number, strobogrammatic prime,[13] alternating factorial[14]
620s
[edit]- 620 = 22 × 5 × 31, sum of four consecutive primes (149 + 151 + 157 + 163), sum of eight consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), the sum of the first 620 primes is itself prime[15]
- 621 = 33 × 23, Harshad number, the discriminant of a totally real cubic field[16]
- 622 = 2 × 311, nontotient, Fine number, Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree, it is also the standard diameter of modern road bicycle wheels (622 mm, from hook bead to hook bead)
- 623 = 7 × 89, number of partitions of 23 into an even number of parts[17]
- 624 = 24 × 3 × 13 = J4(5),[18] sum of a twin prime pair (311 + 313), Harshad number, Zuckerman number
- 625 = 252 = 54, sum of seven consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103), centered octagonal number,[19] 1-automorphic number, Friedman number since 625 = 56−2,[20] one of the two three-digit numbers when squared or raised to a higher power that end in the same three digits, the other being 376
- 626 = 2 × 313, nontotient, 2-Knödel number, Stitch's experiment number
- 627 = 3 × 11 × 19, sphenic number, number of integer partitions of 20,[21] Smith number[22]
- 628 = 22 × 157, nontotient, totient sum for first 45 integers
- 629 = 17 × 37, highly cototient number,[23] Harshad number, number of diagonals in a 37-gon[24]
630s
[edit]- 630 = 2 × 32 × 5 × 7, sum of six consecutive primes (97 + 101 + 103 + 107 + 109 + 113), triangular number, hexagonal number,[25] sparsely totient number,[26] Harshad number, balanced number,[27] largely composite number[2]
- 631 = Cuban prime number, Lucky prime, centered triangular number,[28] centered hexagonal number,[29] Chen prime, lazy caterer number (sequence A000124 in the OEIS)
- 632 = 23 × 79, refactorable number, number of 13-bead necklaces with 2 colors[30]
- 633 = 3 × 211, sum of three consecutive primes (199 + 211 + 223), Blum integer; also, in the title of the movie 633 Squadron
- 634 = 2 × 317, nontotient, Smith number[22]
- 635 = 5 × 127, sum of nine consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), Mertens function(635) = 0, number of compositions of 13 into pairwise relatively prime parts[31]
- 636 = 22 × 3 × 53, sum of ten consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), Smith number,[22] Mertens function(636) = 0
- 637 = 72 × 13, Mertens function(637) = 0, decagonal number[32]
- 638 = 2 × 11 × 29, sphenic number, sum of four consecutive primes (151 + 157 + 163 + 167), nontotient, centered heptagonal number[33]
- 639 = 32 × 71, sum of the first twenty primes, also ISO 639 is the ISO's standard for codes for the representation of languages
640s
[edit]- 640 = 27 × 5, Harshad number, refactorable number, hexadecagonal number,[34] number of 1's in all partitions of 24 into odd parts,[35] number of acres in a square mile
- 641 = prime number, Sophie Germain prime,[36] factor of 4294967297 (the smallest nonprime Fermat number), Chen prime, Eisenstein prime with no imaginary part, Proth prime[37]
- 642 = 2 × 3 × 107 = 14 + 24 + 54,[38] sphenic number, admirable number
- 643 = prime number, largest prime factor of 123456
- 644 = 22 × 7 × 23, nontotient, Perrin number,[39] Harshad number, common umask, admirable number
- 645 = 3 × 5 × 43, sphenic number, octagonal number, Smith number,[22] Fermat pseudoprime to base 2,[40] Harshad number
- 646 = 2 × 17 × 19, sphenic number, also ISO 646 is the ISO's standard for international 7-bit variants of ASCII, number of permutations of length 7 without rising or falling successions[41]
- 647 = prime number, sum of five consecutive primes (113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part, 3647 - 2647 is prime[42]
- 648 = 23 × 34 = A331452(7, 1),[6] Harshad number, Achilles number, area of a square with diagonal 36[43]
- 649 = 11 × 59, Blum integer
650s
[edit]- 650 = 2 × 52 × 13, primitive abundant number,[44] square pyramidal number,[45] pronic number,[1] nontotient, totient sum for first 46 integers; (other fields) the number of seats in the House of Commons of the United Kingdom, admirable number
- 651 = 3 × 7 × 31, sphenic number, pentagonal number,[46] nonagonal number[47]
- 652 = 22 × 163, maximal number of regions by drawing 26 circles[48]
- 653 = prime number, Sophie Germain prime,[36] balanced prime,[4] Chen prime, Eisenstein prime with no imaginary part
- 654 = 2 × 3 × 109, sphenic number, nontotient, Smith number,[22] admirable number
- 655 = 5 × 131, number of toothpicks after 20 stages in a three-dimensional grid[49]
- 656 = 24 × 41 = ,[50] in Judaism, 656 is the number of times that Jerusalem is mentioned in the Hebrew Bible or Old Testament
- 657 = 32 × 73, the largest known number not of the form a2+s with s a semiprime
- 658 = 2 × 7 × 47, sphenic number, untouchable number
- 659 = prime number, Sophie Germain prime,[36] sum of seven consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107), Chen prime, Mertens function sets new low of −10 which stands until 661, highly cototient number,[23] Eisenstein prime with no imaginary part, strictly non-palindromic number[5]
660s
[edit]- 660 = 22 × 3 × 5 × 11
- Sum of four consecutive primes (157 + 163 + 167 + 173)
- Sum of six consecutive primes (101 + 103 + 107 + 109 + 113 + 127)
- Sum of eight consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101)
- Sparsely totient number[26]
- Sum of 11th row when writing the natural numbers as a triangle.[51]
- Harshad number.
- largely composite number[2]
- 661 = prime number
- Sum of three consecutive primes (211 + 223 + 227)
- Mertens function sets new low of −11 which stands until 665
- Pentagram number of the form
- Hexagram number of the form i.e. a star number
- 662 = 2 × 331, nontotient, member of Mian–Chowla sequence[52]
- 663 = 3 × 13 × 17, sphenic number, Smith number[22]
- 664 = 23 × 83, refactorable number, number of knapsack partitions of 33[53]
- Telephone area code for Montserrat
- Area code for Tijuana within Mexico
- Model number for the Amstrad CPC 664 home computer
- 665 = 5 × 7 × 19, sphenic number, Mertens function sets new low of −12 which stands until 1105, number of diagonals in a 38-gon[24]
- 666 = 2 × 32 × 37, 36th triangular number, Harshad number, repdigit
- 667 = 23 × 29, lazy caterer number (sequence A000124 in the OEIS)
- 668 = 22 × 167, nontotient
- 669 = 3 × 223, Blum integer
670s
[edit]- 670 = 2 × 5 × 67, sphenic number, octahedral number,[54] nontotient
- 671 = 11 × 61. This number is the magic constant of n×n normal magic square and n-queens problem for n = 11.
- 672 = 25 × 3 × 7, harmonic divisor number,[55] Zuckerman number, admirable number, largely composite number,[2] triperfect number
- 673 = prime number, lucky prime, Proth prime[37]
- 674 = 2 × 337, nontotient, 2-Knödel number
- 675 = 33 × 52, Achilles number
- 676 = 22 × 132 = 262, palindromic square
- 677 = prime number, Chen prime, Eisenstein prime with no imaginary part, number of non-isomorphic self-dual multiset partitions of weight 10[56]
- 678 = 2 × 3 × 113, sphenic number, nontotient, number of surface points of an octahedron with side length 13,[57] admirable number
- 679 = 7 × 97, sum of three consecutive primes (223 + 227 + 229), sum of nine consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), smallest number of multiplicative persistence 5[58]
680s
[edit]- 680 = 23 × 5 × 17, tetrahedral number,[59] nontotient
- 681 = 3 × 227, centered pentagonal number[3]
- 682 = 2 × 11 × 31, sphenic number, sum of four consecutive primes (163 + 167 + 173 + 179), sum of ten consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), number of moves to solve the Norwegian puzzle strikketoy[60]
- 683 = prime number, Sophie Germain prime,[36] sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part, Wagstaff prime[61]
- 684 = 22 × 32 × 19, Harshad number, number of graphical forest partitions of 32[62]
- 685 = 5 × 137, centered square number[63]
- 686 = 2 × 73, nontotient, number of multigraphs on infinite set of nodes with 7 edges[64]
- 687 = 3 × 229, 687 days to orbit the Sun (Mars) D-number[65]
- 688 = 24 × 43, Friedman number since 688 = 8 × 86,[20] 2-automorphic number[66]
- 689 = 13 × 53, sum of three consecutive primes (227 + 229 + 233), sum of seven consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109). Strobogrammatic number[67]
690s
[edit]- 690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number,[26] Smith number,[22] Harshad number
- ISO 690 is the ISO's standard for bibliographic references
- 691 = prime number, (negative) numerator of the Bernoulli number B12 = -691/2730. Ramanujan's tau function τ and the divisor function σ11 are related by the remarkable congruence τ(n) ≡ σ11(n) (mod 691).
- In number theory, 691 is a "marker" (similar to the radioactive markers in biology): whenever it appears in a computation, one can be sure that Bernoulli numbers are involved.
- 692 = 22 × 173, number of partitions of 48 into powers of 2[68]
- 693 = 32 × 7 × 11, triangular matchstick number,[69] the number of sections in Ludwig Wittgenstein's Philosophical Investigations.
- 694 = 2 × 347, centered triangular number,[28] nontotient, smallest pandigital number in base 5.[70]
- 695 = 5 × 139, 695!! + 2 is prime.[71]
- 696 = 23 × 3 × 29, sum of a twin prime (347 + 349) sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), totient sum for first 47 integers, trails of length 9 on honeycomb lattice[72]
- 697 = 17 × 41, cake number; the number of sides of Colorado[73]
- 698 = 2 × 349, nontotient, sum of squares of two primes[74]
- 699 = 3 × 233, D-number[65]
References
[edit]- ^ 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.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A016038 (Strictly non-palindromic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A331452 (Triangle read by rows: T(n,m) (n >= m >= 1) = number of regions (or cells) formed by drawing the line segments connecting any two of the 2*(m+n) perimeter points of an m X n grid of squares)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000787 (Strobogrammatic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b 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 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 A032020 (Number of compositions (ordered partitions) of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
- ^ Sloane, N. J. A. (ed.). "Sequence A007597 (Strobogrammatic primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005165 (Alternating factorials)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ OEIS: A013916
- ^ Sloane, N. J. A. (ed.). "Sequence A006832 (Discriminants of totally real cubic fields)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A027187 (Number of partitions of n into an even number of parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A059377 (Jordan function J_4(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A036057 (Friedman numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) = number of partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000096 (a(n) = n*(n+3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000031 (Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A101268 (Number of compositions of n into pairwise relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A051868 (16-gonal (or hexadecagonal) numbers: a(n) = n*(7*n-6))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A074501 (a(n) = 1^n + 2^n + 5^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002464 (Hertzsprung's problem: ways to arrange n non-attacking kings on an n X n board, with 1 in each row and column. Also number of permutations of length n without rising or falling successions)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A057468 (Numbers k such that 3^k - 2^k is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001105 (a(n) = 2*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (a(n) = n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A160160 (Toothpick sequence in the three-dimensional grid)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002379 (a(n) = floor(3^n / 2^n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A027480 (a(n) = n*(n+1)*(n+2)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A108917 (Number of knapsack partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A316983 (Number of non-isomorphic self-dual multiset partitions of weight n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron with side n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A003001 (Smallest number of multiplicative persistence n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ 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 A000975 (Lichtenberg sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A000979 (Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
- ^ Sloane, N. J. A. (ed.). "Sequence A000070 (a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ 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 A050535 (Number of multigraphs on infinite set of nodes with n edges)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A033553 (3-Knödel numbers or D-numbers: numbers n > 3 such that n divides k^(n-2)-k for all k with gcd(k, n) = 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A030984 (2-automorphic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-09-01.
- ^ Sloane, N. J. A. (ed.). "Sequence A000787 (Strobogrammatic numbers)". 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. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A045943 (Triangular matchstick numbers: a(n) = 3*n*(n+1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A049363 (a(1) = 1; for n > 1, smallest digitally balanced number in base n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A076185 (Numbers n such that n!! + 2 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A006851 (Trails of length n on honeycomb lattice)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-18.
- ^ "Colorado is a rectangle? Think again". 23 January 2023.
- ^ Sloane, N. J. A. (ed.). "Sequence A045636 (Numbers of the form p^2 + q^2, with p and q primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.