Collatz conjecture

Starting from any positive integer n, repeatedly apply: n → n/2 if n is even, n → 3n+1 if n is odd. The Collatz conjecture states that the sequence always eventually reaches 1.

The problem has been verified by computer for n up to 2^71, and Terence Tao showed in 2019 that 'almost all' starting values eventually fall below any given bound. But a full proof remains elusive.