Recreational Number Theory

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6 domain-specific abstractions whose origin domain is Recreational Number Theory.

• Amenable number — A positive integer n admitting a multiset of exactly n integers whose sum and product are both n.
• Dudeney number — A base-dependent natural number that is a perfect cube whose digit sum equals its cube root.
• Keith number — A natural number whose base-b digits seed a k-step Fibonacci-like recurrence that later reproduces the number.
• Lunar arithmetic — Replace digit addition by maximum and digit multiplication by minimum, extending them positionally without carries so nonnegative base-b numerals form a closed idempotent arithmetic with altered sums, products, factors, and primes.
• Persistence of a number — The number of repeated applications of a specified digit operation needed for an integer to reach a fixed point, most commonly a single digit under repeated digit sums or products.
• Taxicab number — The smallest positive integer expressible as a sum of two positive cubes in a specified number of distinct unordered ways.