Sequences and series | Number theory
Ducci sequence
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 , the next n-tuple in the sequence is formed by taking the absolute differences of neighbouring integers: Another way of describing this is as follows. Arrange n integers in a circle and make a new circle by taking the difference between neighbours, ignoring any minus signs; then repeat the operation. Ducci sequences are named after Enrico Ducci (1864 - 1940), the Italian mathematician who discovered this in the 1930s. Ducci sequences are also known as the Ducci map or the n-number game. Open problems in the study of these maps still remain. (Wikipedia).
