The F Sequence

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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. The Farey sequences of orders 1 to 6 are : F1 = [0/1, 1/1] F2 = [0/1, 1/2, 1/1] F3 = [0/1, 1/3, 1/2, 2/3, 1/1] F4 = [0/1, 1/4, 1/3, 1/2, 2/3, 3/4, 1/1] F5 = [0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2

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