Ducci sequence

Ducci sequences

Given an n-tuple of integers (a1,a2,...,an), a new n-tuple is formed by taking the absolute differences: (|a1-a2|, |a2-a3|, ..., |an-a1|).

It has been proven that one will reach the sequence (0,0,...,0) in a finite number of steps if and only if n is a power of 2.

Source: www.math.jussieu.fr/theses/2002/breuer/homepage/research.html