# Farey sequence

[fair-ee]

- the increasing sequence of fractions in which numerator and denominator have no common divisor other than one and in which the denominator is less than or equal to a given positive integer p. For p = 4, the Farey sequence of order 4 is 0/1, 1/4, 1/3, 1/2, 2/3, 3/4, 1/1.

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## Origin of Farey sequence^{}

after English mathematician John Farey (1766–1826), who proposed the terms of the sequence in 1816

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018