This is a list of recreational number theory topics (see number theory, recreational mathematics). Listing here is not pejorative: many famous topics in number theory have origins in challenging problems posed purely for their own sake.
See list of number theory topics for pages dealing with aspects of number theory with more consolidated theories.
Number sequences
 | This article may contain unverified or indiscriminate information in embedded lists. Please help clean up the lists by removing items or incorporating them into the text of the article. (May 2013) |
- Integer sequence
- Fibonacci sequence
- Lucas sequence
- Padovan sequence
- Figurate numbers
- Polygonal number
- Centered polygonal number
- Tetrahedral number
- Pyramidal number
- Octahedral number
- Star number
- Perfect number
- Untouchable number
- Amicable number
- Sociable number
- Abundant number
- Deficient number
- Amenable number
- Aliquot sequence
- Super-Poulet number
- Lucky number
- Powerful number
- Primeval number
- Palindromic number
- Telephone number
- Triangular square number
- Harmonic divisor number
- Sphenic number
- Smith number
- Double Mersenne number
- Zeisel number
- Heteromecic number
- Niven numbers
- Superparticular number
- Highly composite number
- Highly totient number
- Practical number
- Juggler sequence
- Look-and-say sequence
Digits
- Polydivisible number
- Automorphic number
- Armstrong number
- Self number
- Harshad number
- Keith number
- Kaprekar number
- Digit sum
- Persistence of a number
- Perfect digital invariant
- Perfect digit-to-digit invariant
- Factorion
- Emirp
- Palindromic prime
- Home prime
- Normal number
- Repunit
- Repdigit
Prime and related sequences
- Semiprime
- Almost prime
- Unique prime
- Factorial prime
- Permutable prime
- Palindromic prime
- Cuban prime
- Lucky prime