A sequence of positive integers can be recursively defined as follows: xn+ 1 = 3xn + 1 if xn is odd and xn+ 1 = xn/2 if xn is even. The Collatz conjecture states that that sequence eventually returns to 1 from any initial term x1, e.g. 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. The conjecture is unproven but has been verified for initial terms up to 1020.