Farey Sequence

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The Farey sequence of order n is a sequence of completely reduced fractions between 0 and 1

Excluding the 0 and 1, the number of terms equals the euler’s totient function phi(n)

Order 5

0, 1/5, 2/5, 3/5, 4/5, 1

Given two entries a/b and c/d the next term p/q can be computed as

p = floor((n+b)/d) * c - a
q = floor((n+b)/d) * d - b

Stern Brocot Tree