In mathematics, the Farey sequence of order n is 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.

Each Farey sequence starts with the value 0, denoted by the fraction ⁄₁, and ends with the value 1, denoted by the fraction ⁄₁ (although some authors omit these terms).