Ducci sequence

noun

A sequence of n-tuples of integers (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: (a_1,a_2,...,a_n)→(|a_1-a_2|,|a_2-a_3|,...,|a_n-a_1|),.

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Meanings

nounDucci sequence (plural Ducci sequences)

plural Ducci sequences

  1. mathematicsA sequence of n-tuples of integers (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: (a_1,a_2,...,a_n)→(|a_1-a_2|,|a_2-a_3|,...,|a_n-a_1|),.

Origin

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

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Cite this entry
APA

Ducci sequence. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/Ducci%20sequence

MLA

“Ducci sequence.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Ducci%20sequence. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “Ducci sequence,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/Ducci%20sequence.

Source: Ducci sequence on Wiktionary, CC BY-SA 4.0.