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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.

Contents

• Number sequences
• Digits
• Prime and related sequences
• Magic squares, etc.

See list of number theory topics for pages dealing with aspects of number theory with more consolidated theories.

Number sequences

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• Integer sequence
• Fibonacci sequence
  • Golden mean base
  • Fibonacci coding
• Lucas sequence
• Padovan sequence
• Figurate numbers
  • Polygonal number
    • Triangular number
    • Square number
    • Pentagonal number
    • Hexagonal number
    • Heptagonal number
    • Octagonal number
    • Nonagonal number
    • Decagonal number
  • Centered polygonal number
    • Centered square number
    • Centered pentagonal number
    • Centered hexagonal number
  • Tetrahedral number
  • Pyramidal number
    • Triangular pyramidal number
    • Square pyramidal number
    • Pentagonal pyramidal number
    • Hexagonal pyramidal number
    • Heptagonal pyramidal number
  • Octahedral number
  • Star number
• Perfect number
  • Quasiperfect number
  • Almost perfect number
  • Multiply perfect number
  • Hyperperfect number
  • Semiperfect number
  • Primitive semiperfect number
  • Unitary perfect number
  • Weird 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
  • Happy number
• Perfect digit-to-digit invariant
• Factorion
• Emirp
• Palindromic prime
• Home prime
• Normal number
  • Stoneham number
  • Champernowne constant
  • Absolutely normal number
• Repunit
• Repdigit

Prime and related sequences

• Semiprime
• Almost prime
• Unique prime
• Factorial prime
• Permutable prime
• Palindromic prime
• Cuban prime
• Lucky prime

Magic squares, etc.

• Ulam spiral
• Magic star
• Magic square
  • Frénicle standard form
  • Prime reciprocal magic square
  • Trimagic square
  • Multimagic square
  • Panmagic square
  • Satanic square
  • Most-perfect magic square
  • Geometric magic square
  • Conway's Lux method for magic squares
• Magic cube
  • Perfect magic cube
  • Semiperfect magic cube
  • Bimagic cube
  • Trimagic cube
  • Multimagic cube
• Magic hypercube
• Magic constant
• Squaring the square