Lychrel

Lychrel is a small Python library of number-theory curiosities, written in Rust with PyO3. It works on Python integers of any size.

Function	What it computes
find_lychrel_palindrome	First palindrome of the reverse-and-add process
is_lychrel_candidate	Whether reverse-and-add fails to reach a palindrome
fibonacci	Fibonacci numbers
lucas	Lucas numbers
horadam	Any recurrence W(n) = p·W(n-1) - q·W(n-2), such as Pell or Jacobsthal
look_and_say	Next term of the look-and-say sequence
kaprekar	Fixed point of Kaprekar's routine
collatz	Collatz (3n + 1) sequence

Installation

pip install lychrel

Wheels are published for Linux, macOS, and Windows, and work on any CPython from 3.8 on. On other platforms pip builds from source, which requires a Rust toolchain.

Quick start

import lychrel

lychrel.find_lychrel_palindrome(89)  # (8813200023188, 24)
lychrel.is_lychrel_candidate(196)    # True
lychrel.fibonacci(10)                # 55
lychrel.lucas(10)                    # 123
lychrel.horadam(10, p=2, q=-1)       # 2378 (Pell numbers)
lychrel.look_and_say(1211)           # 111221
lychrel.kaprekar(3524)               # 6174
lychrel.collatz(5)                   # [5, 16, 8, 4, 2, 1]

The reference describes each function, its defaults, and the errors it raises.