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Farey sequence

curriculum/challenges/english/blocks/rosetta-code-challenges/59c3ec9f15068017c96eb8a3.md

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--description--

The Farey sequence <code>F<sub>n</sub></code> 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 sequence is sometimes incorrectly called a Farey series.

Each Farey sequence:

<ul> <li>starts with the value 0, denoted by the fraction $ \frac{0}{1} $</li> <li>ends with the value 1, denoted by the fraction $ \frac{1}{1}$.</li> </ul>

The Farey sequences of orders 1 to 5 are:

<ul> <li style='list-style: none;'>${\bf\it{F}}_1 = \frac{0}{1}, \frac{1}{1}$</li> <li style='list-style: none;'>${\bf\it{F}}_2 = \frac{0}{1}, \frac{1}{2}, \frac{1}{1}$</li> <li style='list-style: none;'>${\bf\it{F}}_3 = \frac{0}{1}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{1}{1}$</li> <li style='list-style: none;'>${\bf\it{F}}_4 = \frac{0}{1}, \frac{1}{4}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{1}{1}$</li> <li style='list-style: none;'>${\bf\it{F}}_5 = \frac{0}{1}, \frac{1}{5}, \frac{1}{4}, \frac{1}{3}, \frac{2}{5}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{1}{1}$</li> </ul>

--instructions--

Write a function that returns the Farey sequence of order n. The function should have one parameter that is n. It should return the sequence as an array.

--hints--

farey should be a function.

js
assert(typeof farey === 'function');

farey(3) should return an array

js
assert(Array.isArray(farey(3)));

farey(3) should return ['0/1','1/3','1/2','2/3','1/1']

js
assert.deepEqual(farey(3),['0/1', '1/3', '1/2', '2/3', '1/1']);

farey(4) should return ['0/1','1/4','1/3','1/2','2/3','3/4','1/1']

js
assert.deepEqual(farey(4), ['0/1', '1/4', '1/3', '1/2', '2/3', '3/4', '1/1']);

farey(5) should return ['0/1','1/5','1/4','1/3','2/5','1/2','3/5','2/3','3/4','4/5','1/1']

js
assert.deepEqual(farey(5), [
  '0/1',
  '1/5',
  '1/4',
  '1/3',
  '2/5',
  '1/2',
  '3/5',
  '2/3',
  '3/4',
  '4/5',
  '1/1'
]);

--seed--

--seed-contents--

js
function farey(n) {

}

--solutions--

js
function farey(n) {
  const sequence = [{ string: "0/1", float: 0.0 }];
  for (let i = 1; i < n; i++) {
    for (let j = n; j >= i; j--) {
      if (i === 1 || j % i > 0) {
        sequence.push({ string: `${i}/${j}`, float: i / j });
      }
    }
  }
  return sequence
    .sort((a, b) => a.float - b.float)
    .map(e => e.string)
}