Phrase guide

Farey sequence

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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1

noun

Meaning 1

For a given positive integer n, the sequence of completely reduced fractions between 0 and 1 which, when in lowest terms, have denominators less than or equal to n, arranged in order of increasing size.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, number-theory, sciences

Examples

  • 2007, Jakub Pawlewicz, Order Statistics in the Farey Sequences in Sublinear Time, Lars Arge, Michael Hoffmann, Emo Welzl (editors), Algorithms - ESA 2007: 15th Annual European Symposium, Proceedings, Springer, LNCS 4698, page 218, The Farey sequence of order n (denoted Fn) is the increasing sequence of all irreducible fractions from interval [0,1] with denominators less than or equal to n. The Farey sequences have numerous interesting properties and they are well known in the number theory and in the combinatorics.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Named after British geologist John Farey Sr., whose letter about the sequences was published in the Philosophical Magazine in 1816.