Ducci sequence

Named after Italian mathematician Enrico Ducci (1864–1940), who discovered in the 1930s that every such sequence eventually becomes periodic.

Ducci sequence (plural Ducci sequences)

1. (mathematics) A sequence of n-tuples of integers ${\displaystyle (a_{1},a_{2},...,a_{n})}$, such that the next n-tuple in the sequence is formed by taking the absolute differences of neighbouring integers: ${\displaystyle (a_{1},a_{2},...,a_{n})\rightarrow (|a_{1}-a_{2}|,|a_{2}-a_{3}|,...,|a_{n}-a_{1}|)\,.}$