2015-3: Farey Tale
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 0⁄1, and ends with the value 1, denoted by the fraction 1⁄1.
Write a function that takes an integer right argument and returns a vector of the terms in the Farey sequence of that order. Each element in the returned vector is itself a 2-element vector of numerator and denominator for the corresponding term.
Examples:
(your_function) 0
┌───┐
│0 1│
└───┘
(your_function) 1
┌───┬───┐
│0 1│1 1│
└───┴───┘
(your_function) 5
┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
│0 1│1 5│1 4│1 3│2 5│1 2│3 5│2 3│3 4│4 5│1 1│
└───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘
your_function ←
Solutions
