This article provides a list of integer sequences in the OnLine Encyclopedia of Integer Sequences that have their own English Wikipedia entries.
OEIS link  Name  First elements  Short description 

A000002  Kolakoski sequence  {1, 2, 2, 1, 1, 2, 1, 2, 2, 1, ...}  The nth term describes the length of the nth run 
A000010  Euler's totient function φ(n)  {1, 1, 2, 2, 4, 2, 6, 4, 6, 4, ...}  φ(n) is the number of positive integers not greater than n that are prime to n. 
A000027  Natural numbers  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}  The natural numbers (positive integers) n ∈ ℕ. 
A000032  Lucas numbers L(n)  {2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ...}  L(n) = L(n − 1) + L(n − 2) for n ≥ 2, with L(0) = 2 and L(1) = 1. 
A000040  Prime numbers p_{n}  {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...}  The prime numbers p_{n}, with n ≥ 1. 
A000041  Partition numbers P_{n} 
{1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, ...}  The partition numbers, number of additive breakdowns of n. 
A000043  Mersenne prime exponents  {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ...}  Primes p such that 2^{p} − 1 is prime. 
A000045  Fibonacci numbers F(n)  {0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...}  F(n) = F(n − 1) + F(n − 2) for n ≥ 2, with F(0) = 0 and F(1) = 1. 
A000058  Sylvester's sequence  {2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, ...}  a(n + 1) = a(n)⋅a(n − 1)⋅ ⋯ ⋅a(0) + 1 = a(n)^{2} − a(n) + 1 for n ≥ 1, with a(0) = 2. 
A000073  Tribonacci numbers  {0, 1, 1, 2, 4, 7, 13, 24, 44, 81, ...}  T(n) = T(n − 1) + T(n − 2) + T(n − 3) for n ≥ 3, with T(0) = 0 and T(1) = T(2) = 1. 
A000105  Polyominoes  {1, 1, 1, 2, 5, 12, 35, 108, 369, ...}  The number of free polyominoes with n cells. 
A000108  Catalan numbers C_{n}  {1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, ...}  
A000110  Bell numbers B_{n}  {1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, ...}  B_{n} is the number of partitions of a set with n elements. 
A000111  Euler zigzag numbers E_{n}  {1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, ...}  E_{n} is the number of linear extensions of the "zigzag" poset. 
A000124  Lazy caterer's sequence  {1, 2, 4, 7, 11, 16, 22, 29, 37, 46, ...}  The maximal number of pieces formed when slicing a pancake with n cuts. 
A000129  Pell numbers P_{n}  {0, 1, 2, 5, 12, 29, 70, 169, 408, 985, ...}  a(n) = 2a(n − 1) + a(n − 2) for n ≥ 2, with a(0) = 0, a(1) = 1. 
A000142  Factorials n!  {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, ...}  n! := 1⋅2⋅3⋅4⋅ ⋯ ⋅n for n ≥ 1, with 0! = 1 (empty product). 
A000166  Derangements  {1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, ...}  Number of permutations of n elements with no fixed points. 
A000203  Divisor function σ(n)  {1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, ...}  σ(n) := σ_{1}(n) is the sum of divisors of a positive integer n. 
A000215  Fermat numbers F_{n}  {3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 340282366920938463463374607431768211457, ...}  F_{n} = 2^{2n} + 1 for n ≥ 0. 
A000217  Triangular numbers t(n)  {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, ...}  t(n) = C(n + 1, 2) = n (n + 1)/2 = 1 + 2 + ⋯ + n for n ≥ 1, with t(0) = 0 (empty sum). 
A000238  Polytrees  {1, 1, 3, 8, 27, 91, 350, 1376, 5743, 24635, 108968, ...}  Number of oriented trees with n nodes. 
A000290  Square numbers n^{2}  {0, 1, 4, 9, 16, 25, 36, 49, 64, 81, ...}  n^{2} = n × n 
A000292  Tetrahedral numbers T(n)  {0, 1, 4, 10, 20, 35, 56, 84, 120, 165, ...}  T(n) is the sum of the first n triangular numbers, with T(0) = 0 (empty sum). 
A000330  Square pyramidal numbers  {0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ...}  n (n + 1)(2n + 1)/6 : The number of stacked spheres in a pyramid with a square base. 
A000396  Perfect numbers  {6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, ...}  n is equal to the sum s(n) = σ(n) − n of the proper divisors of n. 
A000578  Cube numbers n^{3}  {0, 1, 8, 27, 64, 125, 216, 343, 512, 729, ...}  n^{3} = n × n × n 
A000584  Fifth powers  {0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, ...}  n^{5} 
A000668  Mersenne primes  {3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, ...}  2^{p} − 1 is prime, where p is a prime. 
A000793  Landau's function  {1, 1, 2, 3, 4, 6, 6, 12, 15, 20, ...}  The largest order of permutation of n elements. 
A000796  Decimal expansion of π  {3, 1, 4, 1, 5, 9, 2, 6, 5, 3, ...}  Ratio of a circle's circumference to its diameter. 
A000930  Narayana's cows  {1, 1, 1, 2, 3, 4, 6, 9, 13, 19, ...}  The number of cows each year if each cow has one cow a year beginning its fourth year. 
A000931  Padovan sequence  {1, 1, 1, 2, 2, 3, 4, 5, 7, 9, ...}  P(n) = P(n − 2) + P(n − 3) for n ≥ 3, with P(0) = P(1) = P(2) = 1. 
A000945  Euclid–Mullin sequence  {2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, ...}  a(1) = 2; a(n + 1) is smallest prime factor of a(1) a(2) ⋯ a(n) + 1. 
A000959  Lucky numbers  {1, 3, 7, 9, 13, 15, 21, 25, 31, 33, ...}  A natural number in a set that is filtered by a sieve. 
A001006  Motzkin numbers  {1, 1, 2, 4, 9, 21, 51, 127, 323, 835, ...}  The number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circle. 
A001045  Jacobsthal numbers  {0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, ...}  a(n) = a(n − 1) + 2a(n − 2) for n ≥ 2, with a(0) = 0, a(1) = 1. 
A001065  Sum of proper divisors s(n)  {0, 1, 1, 3, 1, 6, 1, 7, 4, 8, ...}  s(n) = σ(n) − n is the sum of the proper divisors of the positive integer n. 
A001113  Decimal expansion of e  {2, 7, 1, 8, 2, 8, 1, 8, 2, 8, ...}  Euler's number in base 10. 
A001190  Wedderburn–Etherington numbers  {0, 1, 1, 1, 2, 3, 6, 11, 23, 46, ...}  The number of binary rooted trees (every node has outdegree 0 or 2) with n endpoints (and 2n − 1 nodes in all). 
A001220  Wieferich primes  {1093, 3511}  Primes satisfying 2^{p1} ≡ 1 (mod p^{2}). 
A001263  Narayana numbers  {1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 20, 10, 1, ...}  read by rows. 
A001316  Gould's sequence  {1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, ...}  Number of odd entries in row n of Pascal's triangle. 
A001358  Semiprimes  {4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ...}  Products of two primes, not necessarily distinct. 
A001462  Golomb sequence  {1, 2, 2, 3, 3, 4, 4, 4, 5, 5, ...}  a(n) is the number of times n occurs, starting with a(1) = 1. 
A001608  Perrin numbers P_{n}  {3, 0, 2, 3, 2, 5, 5, 7, 10, 12, ...}  P(n) = P(n−2) + P(n−3) for n ≥ 3, with P(0) = 3, P(1) = 0, P(2) = 2. 
A001620  Euler–Mascheroni constant γ  {5, 7, 7, 2, 1, 5, 6, 6, 4, 9, ...}  
A001622  Decimal expansion of the golden ratio φ  {1, 6, 1, 8, 0, 3, 3, 9, 8, 8, ...}  φ = 1 + √5/2 = 1.6180339887... in base 10. 
A002064  Cullen numbers C_{n}  {1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, ...}  C_{n} = n⋅2^{n} + 1, with n ≥ 0. 
A002110  Primorials p_{n}#  {1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, ...}  p_{n}#, the product of the first n primes. 
A002113  Palindromic numbers  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...}  A number that remains the same when its digits are reversed. 
A002182  Highly composite numbers  {1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ...}  A positive integer with more divisors than any smaller positive integer. 
A002193  Decimal expansion of √2  {1, 4, 1, 4, 2, 1, 3, 5, 6, 2, ...}  Square root of 2. 
A002201  Superior highly composite numbers  {2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ...}  A positive integer n for which there is an e > 0 such that d(n)/n^{e} ≥ d(k)/k^{e} for all k > 1. 
A002378  Pronic numbers  {0, 2, 6, 12, 20, 30, 42, 56, 72, 90, ...}  2t(n) = n (n + 1), with n ≥ 0. 
A002559  Markov numbers  {1, 2, 5, 13, 29, 34, 89, 169, 194, ...}  Positive integer solutions of x^{2} + y^{2} + z^{2} = 3xyz. 
A002808  Composite numbers  {4, 6, 8, 9, 10, 12, 14, 15, 16, 18, ...}  The numbers n of the form xy for x > 1 and y > 1. 
A002858  Ulam number  {1, 2, 3, 4, 6, 8, 11, 13, 16, 18, ...}  a(1) = 1; a(2) = 2; for n > 2, a(n) is least number > a(n − 1) which is a unique sum of two distinct earlier terms; semiperfect. 
A002863  Prime knots  {0, 0, 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, ...}  The number of prime knots with n crossings. 
A002997  Carmichael numbers  {561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, ...}  Composite numbers n such that a^{n − 1} ≡ 1 (mod n) if a is prime to n. 
A003154  Star numbers  {1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, ...}  The nth star number is S_{n} = 6n(n − 1) + 1. 
A003261  Woodall numbers  {1, 7, 23, 63, 159, 383, 895, 2047, 4607, ...}  n⋅2^{n} − 1, with n ≥ 1. 
A003459  Permutable primes  {2, 3, 5, 7, 11, 13, 17, 31, 37, 71, ...}  The numbers for which every permutation of digits is a prime. 
A003601  Arithmetic numbers  {1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, ...}  An integer for which the average of its positive divisors is also an integer. 
A004490  Colossally abundant numbers  {2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ...}  A number n is colossally abundant iff there is an ε > 0 such that for all k > 1,
where σ denotes the sumofdivisors function. 
A005044  Alcuin's sequence  {0, 0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, ...}  Number of triangles with integer sides and perimeter n. 
A005100  Deficient numbers  {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, ...}  Positive integers n such that σ(n) < 2n. 
A005101  Abundant numbers  {12, 18, 20, 24, 30, 36, 40, 42, 48, 54, ...}  Positive integers n such that σ(n) > 2n. 
A005114  Untouchable numbers  {2, 5, 52, 88, 96, 120, 124, 146, 162, 188, ...}  Cannot be expressed as the sum of all the proper divisors of any positive integer. 
A005150  Lookandsay sequence  {1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211, ...}  A = 'frequency' followed by 'digit'indication. 
A005153  Practical numbers  {1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40...}  All smaller positive integers can be represented as sums of distinct factors of the number. 
A005165  Alternating factorial  {1, 1, 5, 19, 101, 619, 4421, 35899, 326981, 3301819, 36614981, 442386619, 5784634181, 81393657019, ...}  n!  (n1)! + (n2)!  ... 1!. 
A005224  Aronson's sequence  {1, 4, 11, 16, 24, 29, 33, 35, 39, 45, ...}  "t" is the first, fourth, eleventh, ... letter in this sentence, not counting spaces or commas. 
A005235  Fortunate numbers  {3, 5, 7, 13, 23, 17, 19, 23, 37, 61, ...}  The smallest integer m > 1 such that p_{n}# + m is a prime number, where the primorial p_{n}# is the product of the first n prime numbers. 
A005349  Harshad numbers in base 10  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, ...}  A Harshad number in base 10 is an integer that is divisible by the sum of its digits (when written in base 10). 
A005384  Sophie Germain primes  {2, 3, 5, 11, 23, 29, 41, 53, 83, 89, ...}  A prime number p such that 2p + 1 is also prime. 
A005835  Semiperfect numbers  {6, 12, 18, 20, 24, 28, 30, 36, 40, 42, ...}  A natural number n that is equal to the sum of all or some of its proper divisors. 
A006003  Magic constants  {15, 34, 65, 111, 175, 260, ...}  Sum of numbers in any row, column, or diagonal of a magic square of order n = 3, 4, 5, 6, 7, 8, .... 
A006037  Weird numbers  {70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, ...}  A natural number that is abundant but not semiperfect. 
A006842  Farey sequence numerators  {0, 1, 0, 1, 1, 0, 1, 1, 2, 1, ...}  
A006843  Farey sequence denominators  {1, 1, 1, 2, 1, 1, 3, 2, 3, 1, ...}  
A006862  Euclid numbers  {2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, ...}  p_{n}# + 1, i.e. 1 + product of first n consecutive primes. 
A006886  Kaprekar numbers  {1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, ...}  X^{2} = Ab^{n} + B, where 0 < B < b^{n} and X = A + B. 
A007304  Sphenic numbers  {30, 42, 66, 70, 78, 102, 105, 110, 114, 130, ...}  Products of 3 distinct primes. 
A007318  Pascal's triangle  {1, 1, 1, 1, 2, 1, 1, 3, 3, 1, ...}  Pascal's triangle read by rows. 
A007540  Wilson primes  {5, 13, 563}  Primes satisfying (p1)! ≡ 1 (mod p^{2}). 
A007588  Stella octangula numbers  {0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381, ...}  Stella octangula numbers: n (2n^{2} − 1), with n ≥ 0. 
A007770  Happy numbers  {1, 7, 10, 13, 19, 23, 28, 31, 32, 44, ...}  The numbers whose trajectory under iteration of sum of squares of digits map includes 1. 
A007947  Radical of an integer  {1, 2, 3, 2, 5, 6, 7, 2, 3, 10, ...}  The radical of a positive integer n is the product of the distinct prime numbers dividing n. 
A010060  Prouhet–Thue–Morse constant  {0, 1, 1, 0, 1, 0, 0, 1, 1, 0, ...}  
A014080  Factorions  {1, 2, 145, 40585, ...}  A natural number that equals the sum of the factorials of its decimal digits. 
A014577  Regular paperfolding sequence  {1, 1, 0, 1, 1, 0, 0, 1, 1, 1, ...}  At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous sequence. 
A016105  Blum integers  {21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, ...}  Numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4). 
A016114  Circular primes  {2, 3, 5, 7, 11, 13, 17, 37, 79, 113, ...}  The numbers which remain prime under cyclic shifts of digits. 
A018226  Magic numbers  {2, 8, 20, 28, 50, 82, 126, ...}  A number of nucleons (either protons or neutrons) such that they are arranged into complete shells within the atomic nucleus. 
A019279  Superperfect numbers  {2, 4, 16, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056, ...}  Positive integers n for which σ^{2}(n) = σ(σ(n)) = 2n. 
A027641  Bernoulli numbers B_{n}  {1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 5, 0, 691, 0, 7, 0, 3617, 0, 43867, 0, ...}  
A031214  First elements in all OEIS sequences  {1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...}  One of sequences referring to the OEIS itself. 
A033307  Decimal expansion of Champernowne constant  {1, 2, 3, 4, 5, 6, 7, 8, 9, 1, ...}  Formed by concatenating the positive integers. 
A034897  Hyperperfect numbers  {6, 21, 28, 301, 325, 496, 697, ...}  khyperperfect numbers, i.e. n for which the equality n = 1 + k (σ(n) − n − 1) holds. 
A035513  Wythoff array  {1, 2, 4, 3, 7, 6, 5, 11, 10, 9, ...}  A matrix of integers derived from the Fibonacci sequence. 
A036262  Gilbreath's conjecture  {2, 1, 3, 1, 2, 5, 1, 0, 2, 7, ...}  Triangle of numbers arising from Gilbreath's conjecture. 
A037274  Home prime  {1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, ...}  For n ≥ 2, a(n) is the prime that is finally reached when you start with n, concatenate its prime factors (A037276) and repeat until a prime is reached; a(n) = − 1 if no prime is ever reached. 
A046075  Undulating numbers  {101, 121, 131, 141, 151, 161, 171, 181, 191, 202, ...}  A number that has the digit form ababab. 
A046758  Equidigital numbers  {1, 2, 3, 5, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 59, 61, 64, ...}  A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. 
A046760  Extravagant numbers  {4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ...}  A number that has fewer digits than the number of digits in its prime factorization (including exponents). 
A050278  Pandigital numbers  {1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, ...}  Numbers containing the digits 0–9 such that each digit appears exactly once. 
A052486  Achilles numbers  {72, 108, 200, 288, 392, 432, 500, 648, 675, 800, ...}  Positive integers which are powerful but imperfect. 
A054037  Primary pseudoperfect numbers  {2, 6, 42, 1806, 47058, 2214502422, 52495396602, ...}  Satisfies a certain Egyptian fraction. 
A059756  Erdős–Woods numbers  {16, 22, 34, 36, 46, 56, 64, 66, 70, 76, 78, 86, 88, ...}  The length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints. 
A060006  Decimal expansion of Pisot–Vijayaraghavan number  {1, 3, 2, 4, 7, 1, 7, 9, 5, 7, ...}  Real root of x^{3} − x − 1. 
A076336  Sierpinski numbers  {78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, ...}  Odd k for which { k⋅2^{n} + 1 : n ∈ ℕ } consists only of composite numbers. 
A076337  Riesel numbers  {509203, 762701, 777149, 790841, 992077, ...}  Odd k for which { k⋅2^{n} − 1 : n ∈ ℕ } consists only of composite numbers. 
A086747  Baum–Sweet sequence  {1, 1, 0, 1, 1, 0, 0, 1, 0, 1, ...}  a(n) = 1 if the binary representation of n contains no block of consecutive zeros of odd length; otherwise a(n) = 0. 
A088054  Factorial primes  {2, 3, 5, 7, 23, 719, 5039, 39916801, ...}  A prime number that is one less or one more than a factorial (all factorials > 1 are even). 
A088164  Wolstenholme primes  {16843, 2124679}  Primes satisfying . 
A090822  Gijswijt's sequence  {1, 1, 2, 1, 1, 2, 2, 2, 3, 1, ...}  The nth term counts the maximal number of repeated blocks at the end of the subsequence from 1 to n1 
A093112  Carol numbers  {−1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, ...}  
A094683  Juggler sequence  {0, 1, 1, 5, 2, 11, 2, 18, 2, 27, ...}  If n ≡ 0 (mod 2) then ⌊√n⌋ else ⌊n^{3/2}⌋. 
A097942  Highly totient numbers  {1, 2, 4, 8, 12, 24, 48, 72, 144, 240, ...}  Each number k on this list has more solutions to the equation φ(x) = k than any preceding k. 
A100264  Decimal expansion of Chaitin's constant  {0, 0, 7, 8, 7, 4, 9, 9, 6, 9, ...}  Chaitin constant (Chaitin omega number) or halting probability. 
A104272  Ramanujan primes  {2, 11, 17, 29, 41, 47, 59, 67, ...}  The n^{th} Ramanujan prime is the least integer R_{n} for which π(x) − π(x/2) ≥ n, for all x ≥ R_{n}. 
A122045  Euler numbers  {1, 0, −1, 0, 5, 0, −61, 0, 1385, 0, ...}  
A138591  Polite numbers  {3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, ...}  A positive integer that can be written as the sum of two or more consecutive positive integers. 
A182369  8675309/Jenny  {8, 6, 7, 5, 3, 0, 9, ...}  Decimal expansion of (7^(e  1/e)  9)*Pi^2, also known as Jenny's constant. 
A194472  Erdős–Nicolas numbers  {24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, ...}  A number n such that there exists another number m and 
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This page was last edited on 24 September 2019, at 21:11