The Collatz conjecture is a famous unsolved mathematics problem. The conjecture asks if two repeating arithmetic operations on any given positive integer will eventually produce the number 1.
Theorized by Lothar Collatz, the conjecture has been proven for all positive integers up to 2.36×1021, but no formal proof exists.
Consider the following operations:
- If the number is even, divide it by two.
- If the number is odd, triple it and add one.
More formally:
Now form a sequence of numbers by repeating this operation, starting with any given positive integer. The Collatz conjecture states that this process will eventually reach the number 1, regardless of which positive integer is initially selected.
If the conjecture is false, then there must be some starting number which produces a sequence that does not contain 1. Such a sequence would either enter a repeating cycle that excludes 1 or increase without bound.
No such sequence has been found.