Farey sequence

[ fair-ee ]

noun

, Mathematics.

1. 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.

Word History and Origins

Origin of Farey sequence¹

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