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