A Ducci sequence is a sequence of n-tuples of integers, sometimes known as "the Diffy game", because it is based on sequences. Given an n-tuple of integers (a_1, a_2, ... a_n) the next n-tuple in the sequence is formed by taking the absolute differences of neighboring integers. Ducci sequences are named after Enrico Ducci (1864-1940), the Italian mathematician credited with their discovery.
Some Ducci sequences descend to all zeroes or a repeating sequence. An example is (1,2,1,2,1,0) -> (1,1,1,1,1,1) -> (0,0,0,0,0,0).