Recursion: Farey Sequence

The Farey sequence of order n is the set of all fractions with a denominator between 1 and n (reduced to its lowest terms and ordered ascendingly). Given an n, write a function that returns the Farey sequence as an array with a string representation of each fraction of the form "numerator/denominator".

Examples

farey(1) ➞ ["0/1", "1/1"]

farey(5) ➞ ["0/1", "1/5", "1/4", "1/3", "2/5", "1/2", "3/5", "2/3", "3/4", "4/5", "1/1"]

farey(7) ➞ ["0/1", "1/7", "1/6", "1/5", "1/4", "2/7", "1/3", "2/5", "3/7", "1/2", "4/7", "3/5", "2/3", "5/7", "3/4", "4/5", "5/6", "6/7", "1/1"]

Notes

• The sequence should always start with "0/1" and end with "1/1".
• It is expected from the challenge-takers to come up with a solution using the concept of recursion or the so-called recursive approach.
• There will be no exceptions to handle, all inputs are positive integers.
• A recursive approach is prone to Uncaught RangeError or exceededing the maximum call size of the stack.
• Optional: Try to solve this with the least lines of code.
• If you think recursion is fun, you can find a collection of those challenges here.