Farey fraction | Farey series | vulgar series

The Farey sequence F_n for any positive integer n is the set of irreducible rational numbers a/b with 0<=a<=b<=n and (a, b) = 1 arranged in increasing order. The first few are F_1 | = | {0/1, 1/1} F_2 | = | {0/1, 1/2, 1/1} F_3 | = | {0/1, 1/3, 1/2, 2/3, 1/1} F_4 | = | {0/1, 1/4, 1/3, 1/2, 2/3, 3/4, 1/1} F_5 | = | {0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1} (OEIS A006842 and A006843). Except for F_1, each F_n has an odd number of terms and the middle term is always 1/2.

Ford circle | mediant | Minkowski's question mark function | sequence rank | Stern-Brocot tree