<P> This article provides a list of integer sequences in the On - Line Encyclopedia of Integer Sequences that have their own English Wikipedia entries . </P> <Table> <Tr> <Th> OEIS link </Th> <Th> Name </Th> <Th> First elements </Th> <Th> Short description </Th> </Tr> <Tr> <Td> A000002 </Td> <Td> Kolakoski sequence </Td> <Td> (1, 2, 2, 1, 1, 2, 1, 2, 2, 1, ...) </Td> <Td> The nth term describes the length of the nth run </Td> </Tr> <Tr> <Td> A000010 </Td> <Td> Euler's totient function φ (n) </Td> <Td> (1, 1, 2, 2, 4, 2, 6, 4, 6, 4, ...) </Td> <Td> φ (n) is the number of positive integers not greater than n that are prime to n . </Td> </Tr> <Tr> <Td> A000027 </Td> <Td> Natural numbers </Td> <Td> (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...) </Td> <Td> The natural numbers (positive integers) n ∈ N . </Td> </Tr> <Tr> <Td> A000032 </Td> <Td> Lucas numbers L (n) </Td> <Td> (2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ...) </Td> <Td> L (n) = L (n − 1) + L (n − 2) for n ≥ 2, with L (0) = 2 and L (1) = 1 . </Td> </Tr> <Tr> <Td> A000040 </Td> <Td> Prime numbers p </Td> <Td> (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...) </Td> <Td> The prime numbers p, with n ≥ 1 . </Td> </Tr> <Tr> <Td> A000041 </Td> <Td> Partition numbers </Td> <Td> (1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, ...) </Td> <Td> The partition numbers, number of additive breakdowns of n . </Td> </Tr> <Tr> <Td> A000045 </Td> <Td> Fibonacci numbers F (n) </Td> <Td> (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...) </Td> <Td> F (n) = F (n − 1) + F (n − 2) for n ≥ 2, with F (0) = 0 and F (1) = 1 . </Td> </Tr> <Tr> <Td> A000058 </Td> <Td> Sylvester's sequence </Td> <Td> (2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, ...) </Td> <Td> a (n + 1) = a (n) ⋅ a (n − 1) ⋅ ⋯ ⋅ a (0) + 1 = a (n) − a (n) + 1 for n ≥ 1, with a (0) = 2 . </Td> </Tr> <Tr> <Td> A000073 </Td> <Td> Tribonacci numbers </Td> <Td> (0, 1, 1, 2, 4, 7, 13, 24, 44, 81, ...) </Td> <Td> T (n) = T (n − 1) + T (n − 2) + T (n − 3) for n ≥ 3, with T (0) = 0 and T (1) = T (2) = 1 . </Td> </Tr> <Tr> <Td> A000108 </Td> <Td> Catalan numbers C </Td> <Td> (1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, ...) </Td> <Td> 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 .) </Td> </Tr> <Tr> <Td> A000110 </Td> <Td> Bell numbers B </Td> <Td> (1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, ...) </Td> <Td> B is the number of partitions of a set with n elements . </Td> </Tr> <Tr> <Td> A000111 </Td> <Td> Euler zigzag numbers E </Td> <Td> (1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, ...) </Td> <Td> E is the number of linear extensions of the "zig - zag" poset . </Td> </Tr> <Tr> <Td> A000124 </Td> <Td> Lazy caterer's sequence </Td> <Td> (1, 2, 4, 7, 11, 16, 22, 29, 37, 46, ...) </Td> <Td> The maximal number of pieces formed when slicing a pancake with n cuts . </Td> </Tr> <Tr> <Td> A000129 </Td> <Td> Pell numbers P </Td> <Td> (0, 1, 2, 5, 12, 29, 70, 169, 408, 985, ...) </Td> <Td> a (n) = 2a (n − 1) + a (n − 2) for n ≥ 2, with a (0) = 0, a (1) = 1 . </Td> </Tr> <Tr> <Td> A000142 </Td> <Td> Factorials n! </Td> <Td> (1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, ...) </Td> <Td> n!: = 1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ ⋯ ⋅ n for n ≥ 1, with 0! = 1 (empty product). </Td> </Tr> <Tr> <Td> A000203 </Td> <Td> Divisor function σ (n) </Td> <Td> (1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, ...) </Td> <Td> σ (n): = σ (n) is the sum of divisors of a positive integer n . </Td> </Tr> <Tr> <Td> A000215 </Td> <Td> Fermat numbers F </Td> <Td> (3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 340282366920938463463374607431768211457, ...) </Td> <Td> F = 2 + 1 for n ≥ 0 . </Td> </Tr> <Tr> <Td> A000217 </Td> <Td> Triangular numbers t (n) </Td> <Td> (0, 1, 3, 6, 10, 15, 21, 28, 36, 45, ...) </Td> <Td> t (n) = C (n + 1, 2) = n (n + 1) / 2 = 1 + 2 + ⋯ + n for n ≥ 1, with t (0) = 0 (empty sum). </Td> </Tr> <Tr> <Td> A000290 </Td> <Td> Square numbers n </Td> <Td> (0, 1, 4, 9, 16, 25, 36, 49, 64, 81, ...) </Td> <Td> n = n × n </Td> </Tr> <Tr> <Td> A000292 </Td> <Td> Tetrahedral numbers T (n) </Td> <Td> (0, 1, 4, 10, 20, 35, 56, 84, 120, 165, ...) </Td> <Td> T (n) is the sum of the first n triangular numbers, with T (0) = 0 (empty sum). </Td> </Tr> <Tr> <Td> A000330 </Td> <Td> Square pyramidal numbers </Td> <Td> (0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ...) </Td> <Td> n (n + 1) (2n + 1) / 6: The number of stacked spheres in a pyramid with a square base . </Td> </Tr> <Tr> <Td> A000396 </Td> <Td> Perfect numbers </Td> <Td> (6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, ...) </Td> <Td> n is equal to the sum s (n) = σ (n) − n of the proper divisors of n . </Td> </Tr> <Tr> <Td> A000578 </Td> <Td> Cube numbers n </Td> <Td> (0, 1, 8, 27, 64, 125, 216, 343, 512, 729, ...) </Td> <Td> n = n × n × n </Td> </Tr> <Tr> <Td> A000668 </Td> <Td> Mersenne primes </Td> <Td> (3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, ...) </Td> <Td> 2 − 1 is prime, where p is a prime . </Td> </Tr> <Tr> <Td> A000793 </Td> <Td> Landau's function </Td> <Td> (1, 1, 2, 3, 4, 6, 6, 12, 15, 20, ...) </Td> <Td> The largest order of permutation of n elements . </Td> </Tr> <Tr> <Td> A000796 </Td> <Td> Decimal expansion of π </Td> <Td> (3, 1, 4, 1, 5, 9, 2, 6, 5, 3, ...) </Td> <Td> Ratio of a circle's circumference to its diameter . </Td> </Tr> <Tr> <Td> A000930 </Td> <Td> Narayana's cows </Td> <Td> (1, 1, 1, 2, 3, 4, 6, 9, 13, 19, ...) </Td> <Td> The number of cows each year if each cow has one cow a year beginning its fourth year . </Td> </Tr> <Tr> <Td> A000931 </Td> <Td> Padovan sequence </Td> <Td> (1, 1, 1, 2, 2, 3, 4, 5, 7, 9, ...) </Td> <Td> P (n) = P (n − 2) + P (n − 3) for n ≥ 3, with P (0) = P (1) = P (2) = 1 . </Td> </Tr> <Tr> <Td> A000945 </Td> <Td> Euclid--Mullin sequence </Td> <Td> (2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, ...) </Td> <Td> a (1) = 2; a (n + 1) is smallest prime factor of a (1) a (2) ⋯ a (n) + 1 . </Td> </Tr> <Tr> <Td> A000959 </Td> <Td> Lucky numbers </Td> <Td> (1, 3, 7, 9, 13, 15, 21, 25, 31, 33, ...) </Td> <Td> A natural number in a set that is filtered by a sieve . </Td> </Tr> <Tr> <Td> A001006 </Td> <Td> Motzkin numbers </Td> <Td> (1, 1, 2, 4, 9, 21, 51, 127, 323, 835, ...) </Td> <Td> The number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circle . </Td> </Tr> <Tr> <Td> A001045 </Td> <Td> Jacobsthal numbers </Td> <Td> (0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, ...) </Td> <Td> a (n) = a (n − 1) + 2a (n − 2) for n ≥ 2, with a (0) = 0, a (1) = 1 . </Td> </Tr> <Tr> <Td> A001065 </Td> <Td> Sum of proper divisors s (n) </Td> <Td> (0, 1, 1, 3, 1, 6, 1, 7, 4, 8, ...) </Td> <Td> s (n) = σ (n) − n is the sum of the proper divisors of the positive integer n . </Td> </Tr> <Tr> <Td> A001113 </Td> <Td> Decimal expansion of e </Td> <Td> (2, 7, 1, 8, 2, 8, 1, 8, 2, 8, ...) </Td> <Td> Euler's number in base 10 . </Td> </Tr> <Tr> <Td> A001190 </Td> <Td> Wedderburn--Etherington numbers </Td> <Td> (0, 1, 1, 1, 2, 3, 6, 11, 23, 46, ...) </Td> <Td> The number of binary rooted trees (every node has out - degree 0 or 2) with n endpoints (and 2n − 1 nodes in all). </Td> </Tr> <Tr> <Td> A001263 </Td> <Td> Narayana numbers </Td> <Td> (1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 20, 10, 1, ...) </Td> <Td> 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 . </Td> </Tr> <Tr> <Td> A001358 </Td> <Td> Semiprimes </Td> <Td> (4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ...) </Td> <Td> Products of two primes, not necessarily distinct . </Td> </Tr> <Tr> <Td> A001462 </Td> <Td> Golomb sequence </Td> <Td> (1, 2, 2, 3, 3, 4, 4, 4, 5, 5, ...) </Td> <Td> a (n) is the number of times n occurs, starting with a (1) = 1 . </Td> </Tr> <Tr> <Td> A001608 </Td> <Td> Perrin numbers P </Td> <Td> (3, 0, 2, 3, 2, 5, 5, 7, 10, 12, ...) </Td> <Td> P (n) = P (n − 2) + P (n − 3) for n ≥ 3, with P (0) = 3, P (1) = 0, P (2) = 2 . </Td> </Tr> <Tr> <Td> A001620 </Td> <Td> Euler--Mascheroni constant γ </Td> <Td> (5, 7, 7, 2, 1, 5, 6, 6, 4, 9, ...) </Td> <Td> 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 .) </Td> </Tr> <Tr> <Td> A001622 </Td> <Td> Decimal expansion of the golden ratio φ </Td> <Td> (1, 6, 1, 8, 0, 3, 3, 9, 8, 8, ...) </Td> <Td> φ = 1 + √ 5 / 2 = 1.6180339887...in base 10 . </Td> </Tr> <Tr> <Td> A002064 </Td> <Td> Cullen numbers C </Td> <Td> (1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, ...) </Td> <Td> C = n ⋅ 2 + 1, with n ≥ 0 . </Td> </Tr> <Tr> <Td> A002110 </Td> <Td> Primorials p #</Td> <Td> (1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, ...) </Td> <Td> p #, the product of the first n primes . </Td> </Tr> <Tr> <Td> A002113 </Td> <Td> Palindromic numbers </Td> <Td> (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...) </Td> <Td> A number that remains the same when its digits are reversed . </Td> </Tr> <Tr> <Td> A002182 </Td> <Td> Highly composite numbers </Td> <Td> (1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ...) </Td> <Td> A positive integer with more divisors than any smaller positive integer . </Td> </Tr> <Tr> <Td> A002193 </Td> <Td> Decimal expansion of √ 2 </Td> <Td> (1, 4, 1, 4, 2, 1, 3, 5, 6, 2, ...) </Td> <Td> Square root of 2 . </Td> </Tr> <Tr> <Td> A002201 </Td> <Td> Superior highly composite numbers </Td> <Td> (2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ...) </Td> <Td> A positive integer n for which there is an e> 0 such that d (n) / n ≥ d (k) / k for all k> 1 . </Td> </Tr> <Tr> <Td> A002378 </Td> <Td> Pronic numbers </Td> <Td> (0, 2, 6, 12, 20, 30, 42, 56, 72, 90, ...) </Td> <Td> 2t (n) = n (n + 1), with n ≥ 0 . </Td> </Tr> <Tr> <Td> A002559 </Td> <Td> Markov numbers </Td> <Td> (1, 2, 5, 13, 29, 34, 89, 169, 194, ...) </Td> <Td> Positive integer solutions of x + y + z = 3xyz . </Td> </Tr> <Tr> <Td> A002808 </Td> <Td> Composite numbers </Td> <Td> (4, 6, 8, 9, 10, 12, 14, 15, 16, 18, ...) </Td> <Td> The numbers n of the form xy for x> 1 and y> 1 . </Td> </Tr> <Tr> <Td> A002858 </Td> <Td> Ulam number </Td> <Td> (1, 2, 3, 4, 6, 8, 11, 13, 16, 18, ...) </Td> <Td> 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 . </Td> </Tr> <Tr> <Td> A002997 </Td> <Td> Carmichael numbers </Td> <Td> (561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, ...) </Td> <Td> Composite numbers n such that a ≡ 1 (mod n) if a is prime to n . </Td> </Tr> <Tr> <Td> A003261 </Td> <Td> Woodall numbers </Td> <Td> (1, 7, 23, 63, 159, 383, 895, 2047, 4607, ...) </Td> <Td> n ⋅ 2 − 1, with n ≥ 1 . </Td> </Tr> <Tr> <Td> A003459 </Td> <Td> Permutable primes </Td> <Td> (2, 3, 5, 7, 11, 13, 17, 31, 37, 71, ...) </Td> <Td> The numbers for which every permutation of digits is a prime . </Td> </Tr> <Tr> <Td> A005044 </Td> <Td> Alcuin's sequence </Td> <Td> (0, 0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, ...) </Td> <Td> Number of triangles with integer sides and perimeter n . </Td> </Tr> <Tr> <Td> A005100 </Td> <Td> Deficient numbers </Td> <Td> (1, 2, 3, 4, 5, 7, 8, 9, 10, 11, ...) </Td> <Td> Positive integers n such that σ (n) <2n . </Td> </Tr> <Tr> <Td> A005101 </Td> <Td> Abundant numbers </Td> <Td> (12, 18, 20, 24, 30, 36, 40, 42, 48, 54, ...) </Td> <Td> Positive integers n such that σ (n)> 2n . </Td> </Tr> <Tr> <Td> A005114 </Td> <Td> Untouchable numbers </Td> <Td> (2, 5, 52, 88, 96, 120, 124, 146, 162, 188, ...) </Td> <Td> Cannot be expressed as the sum of all the proper divisors of any positive integer . </Td> </Tr> <Tr> <Td> A005150 </Td> <Td> Look - and - say sequence </Td> <Td> (1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211, ...) </Td> <Td> A =' frequency' followed by' digit' - indication . </Td> </Tr> <Tr> <Td> A005224 </Td> <Td> Aronson's sequence </Td> <Td> (1, 4, 11, 16, 24, 29, 33, 35, 39, 45, ...) </Td> <Td> "t" is the first, fourth, eleventh,...letter in this sentence, not counting spaces or commas . </Td> </Tr> <Tr> <Td> A005235 </Td> <Td> Fortunate numbers </Td> <Td> (3, 5, 7, 13, 23, 17, 19, 23, 37, 61, ...) </Td> <Td> 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 . </Td> </Tr> <Tr> <Td> A005349 </Td> <Td> Harshad numbers in base 10 </Td> <Td> (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, ...) </Td> <Td> A Harshad number in base 10 is an integer that is divisible by the sum of its digits (when written in base 10). </Td> </Tr> <Tr> <Td> A005384 </Td> <Td> Sophie Germain primes </Td> <Td> (2, 3, 5, 11, 23, 29, 41, 53, 83, 89, ...) </Td> <Td> A prime number p such that 2p + 1 is also prime . </Td> </Tr> <Tr> <Td> A005835 </Td> <Td> Semiperfect numbers </Td> <Td> (6, 12, 18, 20, 24, 28, 30, 36, 40, 42, ...) </Td> <Td> A natural number n that is equal to the sum of all or some of its proper divisors . </Td> </Tr> <Tr> <Td> A006037 </Td> <Td> Weird numbers </Td> <Td> (70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, ...) </Td> <Td> A natural number that is abundant but not semiperfect . </Td> </Tr> <Tr> <Td> A006842 </Td> <Td> Farey sequence numerators </Td> <Td> (0, 1, 0, 1, 1, 0, 1, 1, 2, 1, ...) </Td> <Td> </Td> </Tr> <Tr> <Td> A006843 </Td> <Td> Farey sequence denominators </Td> <Td> (1, 1, 1, 2, 1, 1, 3, 2, 3, 1, ...) </Td> <Td> </Td> </Tr> <Tr> <Td> A006862 </Td> <Td> Euclid numbers </Td> <Td> (2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, ...) </Td> <Td> p #+ 1, i.e. 1 + product of first n consecutive primes . </Td> </Tr> <Tr> <Td> A006886 </Td> <Td> Kaprekar numbers </Td> <Td> (1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, ...) </Td> <Td> X = Ab + B, where 0 <B <b and X = A + B . </Td> </Tr> <Tr> <Td> A007304 </Td> <Td> Sphenic numbers </Td> <Td> (30, 42, 66, 70, 78, 102, 105, 110, 114, 130, ...) </Td> <Td> Products of 3 distinct primes . </Td> </Tr> <Tr> <Td> A007318 </Td> <Td> Pascal's triangle </Td> <Td> (1, 1, 1, 1, 2, 1, 1, 3, 3, 1, ...) </Td> <Td> Pascal's triangle read by rows . </Td> </Tr> <Tr> <Td> A007588 </Td> <Td> Stella octangula numbers </Td> <Td> (0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381, ...) </Td> <Td> Stella octangula numbers: n (2n − 1), with n ≥ 0 . </Td> </Tr> <Tr> <Td> A007770 </Td> <Td> Happy numbers </Td> <Td> (1, 7, 10, 13, 19, 23, 28, 31, 32, 44, ...) </Td> <Td> The numbers whose trajectory under iteration of sum of squares of digits map includes 1 . </Td> </Tr> <Tr> <Td> A007947 </Td> <Td> Radical of an integer </Td> <Td> (1, 2, 3, 2, 5, 6, 7, 2, 3, 10, ...) </Td> <Td> The radical of a positive integer n is the product of the distinct prime numbers dividing n . </Td> </Tr> <Tr> <Td> A010060 </Td> <Td> Prouhet--Thue--Morse constant </Td> <Td> (0, 1, 1, 0, 1, 0, 0, 1, 1, 0, ...) </Td> <Td> τ = ∑ i = 0 ∞ t i 2 i + 1 . (\ displaystyle \ tau = \ sum _ (i = 0) ^ (\ infty) (\ frac (t_ (i)) (2 ^ (i + 1))).) </Td> </Tr> <Tr> <Td> A014080 </Td> <Td> Factorions </Td> <Td> (1, 2, 145, 40585, ...) </Td> <Td> A natural number that equals the sum of the factorials of its decimal digits . </Td> </Tr> <Tr> <Td> A014577 </Td> <Td> Regular paperfolding sequence </Td> <Td> (1, 1, 0, 1, 1, 0, 0, 1, 1, 1, ...) </Td> <Td> At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous sequence . </Td> </Tr> <Tr> <Td> A016114 </Td> <Td> Circular primes </Td> <Td> (2, 3, 5, 7, 11, 13, 17, 37, 79, 113, ...) </Td> <Td> The numbers which remain prime under cyclic shifts of digits . </Td> </Tr> <Tr> <Td> A018226 </Td> <Td> Magic numbers </Td> <Td> (2, 8, 20, 28, 50, 82, 126, ...) </Td> <Td> A number of nucleons (either protons or neutrons) such that they are arranged into complete shells within the atomic nucleus . </Td> </Tr> <Tr> <Td> A019279 </Td> <Td> Superperfect numbers </Td> <Td> (2, 4, 16, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056, ...) </Td> <Td> Positive integers n for which σ (n) = σ (σ (n)) = 2n . </Td> </Tr> <Tr> <Td> A027641 </Td> <Td> Bernoulli numbers B </Td> <Td> (1, - 1, 1, 0, - 1, 0, 1, 0, - 1, 0, 5, 0, - 691, 0, 7, 0, - 3617, 0, 43867, 0, ...) </Td> <Td> </Td> </Tr> <Tr> <Td> A031214 </Td> <Td> First elements in all OEIS sequences </Td> <Td> (1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...) </Td> <Td> One of sequences referring to the OEIS itself . </Td> </Tr> <Tr> <Td> A033307 </Td> <Td> Decimal expansion of Champernowne constant </Td> <Td> (1, 2, 3, 4, 5, 6, 7, 8, 9, 1, ...) </Td> <Td> Formed by concatenating the positive integers . </Td> </Tr> <Tr> <Td> A034897 </Td> <Td> Hyperperfect numbers </Td> <Td> (6, 21, 28, 301, 325, 496, 697, ...) </Td> <Td> k - hyperperfect numbers, i.e. n for which the equality n = 1 + k (σ (n) − n − 1) holds . </Td> </Tr> <Tr> <Td> A035513 </Td> <Td> Wythoff array </Td> <Td> (1, 2, 4, 3, 7, 6, 5, 11, 10, 9, ...) </Td> <Td> A matrix of integers derived from the Fibonacci sequence . </Td> </Tr> <Tr> <Td> A036262 </Td> <Td> Gilbreath's conjecture </Td> <Td> (2, 1, 3, 1, 2, 5, 1, 0, 2, 7, ...) </Td> <Td> Triangle of numbers arising from Gilbreath's conjecture . </Td> </Tr> <Tr> <Td> A037274 </Td> <Td> Home prime </Td> <Td> (1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, ...) </Td> <Td> 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 . </Td> </Tr> <Tr> <Td> A046075 </Td> <Td> Undulating numbers </Td> <Td> (101, 121, 131, 141, 151, 161, 171, 181, 191, 202, ...) </Td> <Td> A number that has the digit form ababab . </Td> </Tr> <Tr> <Td> A050278 </Td> <Td> Pandigital numbers </Td> <Td> (1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, ...) </Td> <Td> Numbers containing the digits 0--9 such that each digit appears exactly once . </Td> </Tr> <Tr> <Td> A052486 </Td> <Td> Achilles numbers </Td> <Td> (72, 108, 200, 288, 392, 432, 500, 648, 675, 800, ...) </Td> <Td> Positive integers which are powerful but imperfect . </Td> </Tr> <Tr> <Td> A060006 </Td> <Td> Decimal expansion of Pisot--Vijayaraghavan number </Td> <Td> (1, 3, 2, 4, 7, 1, 7, 9, 5, 7, ...) </Td> <Td> Real root of x − x − 1 . </Td> </Tr> <Tr> <Td> A076336 </Td> <Td> Sierpinski numbers </Td> <Td> (78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, ...) </Td> <Td> Odd k for which (k ⋅ 2 + 1: n ∈ N) consists only of composite numbers . </Td> </Tr> <Tr> <Td> A076337 </Td> <Td> Riesel numbers </Td> <Td> (509203, 762701, 777149, 790841, 992077, ...) </Td> <Td> Odd k for which (k ⋅ 2 − 1: n ∈ N) consists only of composite numbers . </Td> </Tr> <Tr> <Td> A086747 </Td> <Td> Baum--Sweet sequence </Td> <Td> (1, 1, 0, 1, 1, 0, 0, 1, 0, 1, ...) </Td> <Td> a (n) = 1 if the binary representation of n contains no block of consecutive zeros of odd length; otherwise a (n) = 0 . </Td> </Tr> <Tr> <Td> A090822 </Td> <Td> Gijswijt's sequence </Td> <Td> (1, 1, 2, 1, 1, 2, 2, 2, 3, 1, ...) </Td> <Td> The nth term counts the maximal number of repeated blocks at the end of the subsequence from 1 to n - 1 </Td> </Tr> <Tr> <Td> A094683 </Td> <Td> Juggler sequence </Td> <Td> (0, 1, 1, 5, 2, 11, 2, 18, 2, 27, ...) </Td> <Td> If n ≡ 0 (mod 2) then ⌊ √ n ⌋ else ⌊ n ⌋ . </Td> </Tr> <Tr> <Td> A097942 </Td> <Td> Highly totient numbers </Td> <Td> (1, 2, 4, 8, 12, 24, 48, 72, 144, 240, ...) </Td> <Td> Each number k on this list has more solutions to the equation φ (x) = k than any preceding k . </Td> </Tr> <Tr> <Td> A100264 </Td> <Td> Decimal expansion of Chaitin's constant </Td> <Td> (0, 0, 7, 8, 7, 4, 9, 9, 6, 9, ...) </Td> <Td> Chaitin constant (Chaitin omega number) or halting probability . </Td> </Tr> <Tr> <Td> A104272 </Td> <Td> Ramanujan primes </Td> <Td> (2, 11, 17, 29, 41, 47, 59, 67, ...) </Td> <Td> The n Ramanujan prime is the least integer R for which π (x) − π (x / 2) ≥ n, for all x ≥ R . </Td> </Tr> <Tr> <Td> A122045 </Td> <Td> Euler numbers </Td> <Td> (1, 0, − 1, 0, 5, 0, − 61, 0, 1385, 0, ...) </Td> <Td> 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).) </Td> </Tr> <Tr> <Td> A1238591 </Td> <Td> Polite numbers </Td> <Td> (3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, ...) </Td> <Td> A positive integer that can be written as the sum of two or more consecutive positive integers . </Td> </Tr> </Table> <Tr> <Th> OEIS link </Th> <Th> Name </Th> <Th> First elements </Th> <Th> Short description </Th> </Tr>

What is the sequence of 1 2 6 24