List of OEIS sequences

This article provides a list of integer sequences in the On-Line Encyclopedia of Integer Sequences that have their own Wikipedia entries.

OEIS link Name First elements Short description
A000010 Euler's totient function φ(n) 1, 1, 2, 2, 4, 2, 6, 4, 6, 4 φ(n) is the number of the positive integers not greater than n that are prime to n
A000027 Natural number 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 The natural numbers
A000032 Lucas number 2, 1, 3, 4, 7, 11, 18, 29, 47, 76 L(n) = L(n − 1) + L(n − 2)
A000040 Prime number 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 The prime numbers
A000045 Fibonacci number 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 F(n) = F(n − 1) + F(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)2 − a(n) + 1, with a(0) = 2
A000073 Tribonacci number 0, 1, 1, 2, 4, 7, 13, 24, 44, 81 T(n) = T(n − 1) + T(n − 2) + T(n − 3) with T(0) = 0, T(1) = T(2) = 1
A000108 Catalan number 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862 C_n = \frac{1}{n+1}{2n\choose n} = \frac{(2n)!}{(n+1)!\,n!} = \prod\limits_{k=2}^{n}\frac{n+k}{k} \qquad for n ≥ 0.
A000110 Bell number 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147 The number of partitions of a set with n elements
A000111 Euler number 1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936 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 number 0, 1, 2, 5, 12, 29, 70, 169, 408, 985 a(0) = 0, a(1) = 1; for n > 1, a(n) = 2a(n − 1) + a(n − 2)
A000142 Factorial 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880 n! = 1·2·3·4·...·n
A000203 Divisor function 1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28 Sum of the divisors of a number
A000217 Triangular number 0, 1, 3, 6, 10, 15, 21, 28, 36, 45 a(n) = C(n + 1, 2) = n(n + 1)/2 = 0 + 1 + 2 + ... + n
A000292 Tetrahedral number 0, 1, 4, 10, 20, 35, 56, 84, 120, 165 The sum of the first n triangular numbers
A000330 Square pyramidal number 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 number 6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128 n is equal to the sum of the proper divisors of n
A000668 Mersenne prime 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111 2p − 1 if 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 Pi 3, 1, 4, 1, 5, 9, 2, 6, 5, 3
A000931 Padovan sequence 1, 1, 1, 2, 2, 3, 4, 5, 7, 9 P(0) = P(1) = P(2) = 1, P(n) = P(n−2)+P(n−3)
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 number 1, 3, 7, 9, 13, 15, 21, 25, 31, 33 A natural number in a set that is filtered by a sieve
A001006 Motzkin number 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 number 0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341 a(n) = a(n − 1) + 2a(n − 2), with a(0) = 0, a(1) = 1
A001065 sequence of Aliquot sums s(n) 0, 1, 1, 3, 1, 6, 1, 7, 4, 8 s(n) is the sum of the proper divisors of the integer n
A001113 Decimal expansion of e (mathematical constant) 2, 7, 1, 8, 2, 8, 1, 8, 2, 8
A001190 Wedderburn–Etherington number 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)
A001358 Semiprime 4, 6, 9, 10, 14, 15, 21, 22, 25, 26 Products of two primes
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 number 3, 0, 2, 3, 2, 5, 5, 7, 10, 12 P(0) = 3, P(1) = 0, P(2) = 2; P(n) = P(n−2) + P(n−3) for n > 2
A001620 Euler–Mascheroni constant 5, 7, 7, 2, 1, 5, 6, 6, 4, 9 \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 1, 6, 1, 8, 0, 3, 3, 9, 8, 8 \varphi = \frac{1+\sqrt{5}}{2} = 1.61803\,39887\ldots.
A002064 Cullen number 1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497 n 2n + 1
A002110 Primorial 1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870 The product of first n primes
A002113 Palindromic number 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 A number that remains the same when its digits are reversed
A002182 Highly composite number 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 square root of 2 1, 4, 1, 4, 2, 1, 3, 5, 6, 2
A002201 Superior highly composite number 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)/ne ≥ d(k)/ke for all k>1
A002378 Pronic number 0, 2, 6, 12, 20, 30, 42, 56, 72, 90 n(n+1)
A002808 Composite number 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) = least number > a(n-1) which is a unique sum of two distinct earlier terms; semiperfect
A002997 Carmichael number 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
A003261 Woodall number 1, 7, 23, 63, 159, 383, 895, 2047, 4607 n 2n - 1
A003459 Permutable prime 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 number 1, 2, 3, 4, 5, 7, 8, 9, 10, 11 The numbers n such that σ(n) < 2n
A005101 Abundant number 12, 18, 20, 24, 30, 36, 40, 42, 48, 54 The sum of divisors of n exceeds 2n
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 number 3, 5, 7, 13, 23, 17, 19, 23, 37, 61 The smallest integer m > 1 such that pn# + m is a prime number, where the primorial pn# 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 prime 2, 3, 5, 11, 23, 29, 41, 53, 83, 89 A prime number p such that 2p+1 is also prime
A005835 Semiperfect number 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 number 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 number 2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871 1 + product of first n consecutive primes
A006886 Kaprekar number 1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728 X² = Abn + B, where 0 < B < bn X = A + B
A007304 Sphenic number 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 number 0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381, ... Stella octangula numbers: n*(2*n2 - 1).
A007770 Happy number 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 the 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 \tau = \sum_{i=0}^{\infty} \frac{t_i}{2^{i+1}}
A014080 Factorion 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 prime 2, 3, 5, 7, 11, 13, 17, 37, 79, 113 The numbers which remain prime under cyclic shifts of digits
A018226 Magic number (physics) 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 number 2, 4, 16, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056 \sigma^2(n)=\sigma(\sigma(n))=2n\, ,
A027641 Bernoulli number 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
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) = 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 number 101, 121, 131, 141, 151, 161, 171, 181, 191, 202 A number that has the digit form ababab
A050278 Pandigital number 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 number 72, 108, 200, 288, 392, 432, 500, 648, 675, 800 Powerful but imperfect
A060006 Decimal expansion of Pisot–Vijayaraghavan number 1, 3, 2, 4, 7, 1, 7, 9, 5, 7 real root of x3−x−1
A076336 Sierpinski number 78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909 Odd k for which \left\{\,k 2^n + 1 : n \in\mathbb{N}\,\right\} consists only of composite numbers
A076337 Riesel number 509203, 762701, 777149, 790841, 992077 Odd k for which \left\{\,k 2^n - 1 : n \in\mathbb{N}\,\right\} consists only of composite numbers
A086747 Baum–Sweet sequence 1, 1, 0, 1, 1, 0, 0, 1, 0, 1 a(n) = 1 if binary representation of n contains no block of consecutive zeros of odd length; otherwise a(n) = 0
A094683 Juggler sequence 0, 1, 1, 5, 2, 11, 2, 18, 2, 27 If n mod 2 = 0 then floor(√n) else floor(n3/2)
A097942 Highly totient number 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
A104272 Ramanujan prime 2, 11, 17, 29, 41, 47, 59, 67 The nth Ramanujan prime is the least integer Rn for which \pi(x) - \pi(x/2) ≥ n, for all x ≥ Rn.
A122045 Euler number 1, 0, −1, 0, 5, 0, −61, 0, 1385, 0 \frac{1}{\cosh t} = \frac{2}{e^{t} + e^ {-t} } = \sum_{n=0}^\infty \frac{E_n}{n!} \cdot t^n\!

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