List of integer sequences


This is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences.

Figurate numbers

NameFirst elementsShort descriptionOEIS
Natural numbers1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...The natural numbers .
Triangular numbers 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, ... for, with .
Square numbers 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, ...
Tetrahedral numbers 0, 1, 4, 10, 20, 35, 56, 84, 120, 165, ... is the sum of the first triangular numbers, with .
Square pyramidal numbers0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ...: The number of stacked spheres in a pyramid with a square base.
Cube numbers 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, ...
Fifth powers0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, ...
Star numbers1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, ...Sn = 6n + 1.
Stella octangula numbers0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381, ...Stella octangula numbers:, with.

Types of primes

NameFirst elementsShort descriptionOEIS
Mersenne prime exponents2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ...Primes such that is prime.
Mersenne primes3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, ... is prime, where is a prime.
Wagstaff primes3, 11, 43, 683, 2731, 43691, ...A prime number p of the form where q is an odd prime.
Wieferich primes1093, 3511Primes satisfying.
Sophie Germain primes2, 3, 5, 11, 23, 29, 41, 53, 83, 89, ...A prime number such that is also prime.
Wilson primes5, 13, 563Primes satisfying.
Happy numbers1, 7, 10, 13, 19, 23, 28, 31, 32, 44, ...The numbers whose trajectory under iteration of sum of squares of digits map includes.
Factorial primes2, 3, 5, 7, 23, 719, 5039, 39916801, ...A prime number that is one less or one more than a factorial.
Wolstenholme primes16843, 2124679Primes satisfying.
Ramanujan primes2, 11, 17, 29, 41, 47, 59, 67, ...The th Ramanujan prime is the least integer for which, for all.

Base-dependent

NameFirst elementsShort descriptionOEIS
Aronson's sequence1, 4, 11, 16, 24, 29, 33, 35, 39, 45, ..."t" is the first, fourth, eleventh, ... letter in this sentence, not counting spaces or commas.
Palindromic numbers0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, ...A number that remains the same when its digits are reversed.
Permutable primes2, 3, 5, 7, 11, 13, 17, 31, 37, 71, ...The numbers for which every permutation of digits is a prime.
Harshad numbers in base 101, 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.
Factorions1, 2, 145, 40585, ...A natural number that equals the sum of the factorials of its decimal digits.
Circular primes2, 3, 5, 7, 11, 13, 17, 37, 79, 113, ...The numbers which remain prime under cyclic shifts of digits.
Home prime1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, ...For is the prime that is finally reached when you start with, concatenate its prime factors and repeat until a prime is reached; if no prime is ever reached.
Undulating numbers101, 121, 131, 141, 151, 161, 171, 181, 191, 202, ...A number that has the digit form.
Equidigital numbers1, 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.
Extravagant numbers4, 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.
Pandigital numbers1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, ...Numbers containing the digits such that each digit appears exactly once.