Base-dependent integer sequences

numbers with a certain property involving recursive summation

integer whose representation reads the same forward and backward (in a given numeral system)

integer that is divisible by the sum of its digits

An emirp (pronounced or , an anadrome of prime) is a prime number that results in a different prime when its decimal digits (digits in base 10) are reversed. This definition excludes the related palindromic primes. The term reversible prime is used to mean the same as emirp, but may also, ambiguously, include the palindromic primes.

non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again

In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for "repeated unit" and was coined in 1966 by Albert H. Beiler in his book Recreations in the Theory of Numbers.

prime number that is also a palindromic number

type of composite integer

integer expressible as the sum of the (number of digits)th power of each of its digits

type of composite natural number

In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit". Examples are 11, 666, 4444, and 999999. All repdigits are palindromic numbers and are multiples of repunits. Other well-known repdigits include the repunit primes and in particular the Mersenne primes (which are repdigits when represented in binary).

sum of a number's digits

number

integer sequence

integer that appears as a term in a linear recurrence relation with initial terms based on its own digits

integer expressible as an arrangement of its digits with simple mathematical operations

a natural number whose square "ends" in the same digits as the number itself

a natural number that cannot be written as the sum of any other natural number n and the individual digits of n

repeated digital sum

Integer whose representation contains every digit in its number base

prime number that remains prime after any cyclic permutation of its digits

perfect cube whose cube root is equal to the sum of the original number's digits

prime number that remains prime after any permutation of its digits

In number theory, a factorion in a given number base b is a natural number that equals the sum of the factorials of its digits. The name factorion was coined by the author Clifford A. Pickover.

Type of number

harmonic series with all terms containing the digit '9' removed

number with more digits than its prime factorization

number with fewer digits than its prime factorization

integer obtained by concatenating the first k primes in decimal for some k

integer equal to the sum of each digit in the number raised to itself

b-digit long integer m in a given base b where each digit d at position n counts how many instances of digit n are in m

number in a given base that has the same number of digits as the number of digits in its prime factorization in the given base

natural number which, when multiplied by n, results in movement of the last digit of its decimal representation to its front

Irrational numbers which appear to be rational

prime number where replacing any digit with any other digit results in a composite number

number that has the digit form ababab... in base 10

prime number for which no proper digit subsequence is prime

also known as a dihedral calculator prime

type of natural number in recreational number theory

number with prime Hamming weight