List of OEIS sequences - Wikipedia List of OEIS sequences This article provides a list of integer sequences in the On - Line 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 ( 2, 3, 5, 7, 11, 13, 17, 19, 23, 29,... ) The prime numbers p, with n ≥ 1. A000041 Partition numbers ( 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42,... ) The partition numbers, number of additive breakdowns of n. 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 ) − 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. A000108 Catalan numbers C ( 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862,... ) C n = 1 n + 1 ( 2 n n ) = ( 2 n ) ! ( n + 1 ) ! n ! = ∏ k = 2 n n + k k, n ≥ 0. ( displaystyle C_ ( n ) = ( \frac ( 1 ) ( n + 1 ) ) ( 2n choose n ) = ( \frac ( ( 2n ) ! ) ( ( n + 1 ) ! , n ! ) ) = prod limits _ ( k = 2 ) ^ ( n ) ( \frac ( n + k ) ( k ) ), quad n geq 0. ) A000110 Bell numbers B ( 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147,... ) B is the number of partitions of a set with n elements. A000111 Euler zigzag numbers E ( 1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936,... ) E is the number of linear extensions of the `` zig - zag '' 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 ( 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 ). A000203 Divisor function σ ( n ) ( 1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28,... ) σ ( n ) : = σ ( n ) is the sum of divisors of a positive integer n. A000215 Fermat numbers F ( 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 340282366920938463463374607431768211457,... ) F = 2 + 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 ). A000290 Square numbers n ( 0, 1, 4, 9, 16, 25, 36, 49, 64, 81,... ) n = 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 ( 0, 1, 8, 27, 64, 125, 216, 343, 512, 729,... ) n = n × n × n A000668 Mersenne primes ( 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111,... ) 2 − 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 out - degree 0 or 2 ) with n endpoints ( and 2n − 1 nodes in all ). A001263 Narayana numbers ( 1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 20, 10, 1,... ) 1 k ( n − 1 k − 1 ) ( n k − 1 ) ( displaystyle ( 1 over k ) ( n - 1 choose k - 1 ) ( n choose k - 1 ) ) read by rows. 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 ( 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,... ) γ = lim n → ∞ ( ∑ k = 1 n 1 k − ln ⁡ ( n ) ) = lim b → ∞ ∫ 1 b ( 1 ⌊ x ⌋ − 1 x ) d x. ( displaystyle gamma = lim _ ( n \rightarrow infty ) left ( sum _ ( k = 1 ) ^ ( n ) ( \frac ( 1 ) ( k ) ) - ln ( n ) \right ) = lim _ ( b \rightarrow infty ) int _ ( 1 ) ^ ( b ) left ( ( 1 over lfloor x \rfloor ) - ( 1 over x ) \right ) , dx. ) 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 ( 1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497,... ) C = n ⋅ 2 + 1, with n ≥ 0. A002110 Primorials p # ( 1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870,... ) p #, 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 ≥ d ( k ) / k 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 + y + z = 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. A002997 Carmichael numbers ( 561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341,... ) Composite numbers n such that a ≡ 1 ( mod n ) if a is prime to n. A003261 Woodall numbers ( 1, 7, 23, 63, 159, 383, 895, 2047, 4607,... ) n ⋅ 2 − 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. 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 Look - and - say sequence ( 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211,... ) A = ' frequency ' followed by ' digit ' - indication. 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 # + m is a prime number, where the primorial p # 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. 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 # + 1, i.e. 1 + product of first n consecutive primes. A006886 Kaprekar numbers ( 1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728,... ) X = Ab + B, where 0 < B < b 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. A007588 Stella octangula numbers ( 0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381,... ) Stella octangula numbers : n ( 2n − 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,... ) τ = ∑ i = 0 ∞ t i 2 i + 1. ( displaystyle \tau = sum _ ( i = 0 ) ^ ( infty ) ( \frac ( t_ ( i ) ) ( 2 ^ ( i + 1 ) ) ). ) 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. 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 ( n ) = σ ( σ ( n ) ) = 2n. A027641 Bernoulli numbers B ( 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,... ) k - hyperperfect 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. 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. A060006 Decimal expansion of Pisot -- Vijayaraghavan number ( 1, 3, 2, 4, 7, 1, 7, 9, 5, 7,... ) Real root of x − x − 1. A076336 Sierpinski numbers ( 78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909,... ) Odd k for which ( k ⋅ 2 + 1 : n ∈ N ) consists only of composite numbers. A076337 Riesel numbers ( 509203, 762701, 777149, 790841, 992077,... ) Odd k for which ( k ⋅ 2 − 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. 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 n - 1 A094683 Juggler sequence ( 0, 1, 1, 5, 2, 11, 2, 18, 2, 27,... ) If n ≡ 0 ( mod 2 ) then ⌊ √ n ⌋ else ⌊ n ⌋. 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 Ramanujan prime is the least integer R for which π ( x ) − π ( x / 2 ) ≥ n, for all x ≥ R. A122045 Euler numbers ( 1, 0, − 1, 0, 5, 0, − 61, 0, 1385, 0,... ) 1 cosh ⁡ t = 2 e t + e − t = ∑ n = 0 ∞ E n n ! ⋅ t n. ( displaystyle ( \frac ( 1 ) ( cosh t ) ) = ( \frac ( 2 ) ( e ^ ( t ) + e ^ ( - t ) ) ) = sum _ ( n = 0 ) ^ ( infty ) ( \frac ( E_ ( n ) ) ( n ! ) ) cdot t ^ ( n ). ) A1238591 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. References OEIS core sequences External links Index to OEIS Sequences and series Integer sequences Basic Arithmetic progression Geometric progression Harmonic progression Square number Cubic number Factorial Powers of two Powers of 10 Advanced Complete sequence Fibonacci numbers Figurate number Heptagonal number Hexagonal number Lucas number Pell number Pentagonal number Polygonal number Triangular number Full list Properties of sequences Cauchy sequence Monotone sequence Periodic sequence Properties of series Convergent series Divergent series Conditional convergence Absolute convergence Uniform convergence Alternating series Telescoping series Explicit series Convergent 1 / 2 − 1 / 4 + 1 / 8 − 1 / 16 + ⋯ 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + ⋯ 1 / 4 + 1 / 16 + 1 / 64 + 1 / 256 + ⋯ 1 + 1 / 1 + 1 / 2 + 1 / 3 +... ( Riemann zeta function ) Divergent 1 + 1 + 1 + 1 + ⋯ 1 + 2 + 3 + 4 + ⋯ 1 + 2 + 4 + 8 + ⋯ 1 − 1 + 1 − 1 + ⋯ ( Grandi 's series ) Infinite arithmetic series 1 − 2 + 3 − 4 + ⋯ 1 − 2 + 4 − 8 + ⋯ 1 + 1 / 2 + 1 / 3 + 1 / 4 + ⋯ ( harmonic series ) 1 − 1 + 2 − 6 + 24 − 120 + ⋯ ( alternating factorials ) 1 / 2 + 1 / 3 + 1 / 5 + 1 / 7 + 1 / 11 + ⋯ ( inverses of primes ) Kinds of series Taylor series Power series Formal power series Laurent series Puiseux series Dirichlet series Trigonometric series Fourier series Generating series Hypergeometric series Generalized hypergeometric series Hypergeometric function of a matrix argument Lauricella hypergeometric series Modular hypergeometric series Riemann 's differential equation Theta hypergeometric series Retrieved from `` https://en.wikipedia.org/w/index.php?title=List_of_OEIS_sequences&oldid=793453617 '' Categories : Arithmetic functions Integer sequences Number - related lists Talk About Wikipedia 日本 語 Edit links This page was last edited on 1 August 2017, at 21 : 01. 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Question: what is the sequence of 1 2 6 24
Answer: Factorials n!