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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/farey-sequence.md

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+---
+title: Farey sequence
+id: 59c3ec9f15068017c96eb8a3
+challengeType: 5
+forumTopicId: 302266
+---
+
+## Description
+<section id='description'>
+The  <a href="https://en.wikipedia.org/wiki/Farey sequence" title="wp: Farey sequence" target="_blank">Farey sequence</a>   <code>F<sub>n</sub></code> of order <code>n</code> is the sequence of completely reduced fractions between <code>0</code> and <code>1</code> which, when in lowest terms, have denominators less than or equal to <code>n</code>, arranged in order of increasing size.
+The <i>Farey sequence</i> is sometimes incorrectly called a <i>Farey series</i>.
+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}$.</li>
+</ul>
+The Farey sequences of orders <code>1</code> to <code>5</code> are:
+<ul>
+  <li style="list-style: none;">${\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>
+</section>
+
+## Instructions
+<section id='instructions'>
+Write a function that returns the Farey sequence of order <code>n</code>. The function should have one parameter that is <code>n</code>. It should return the sequence as an array.
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>farey</code> should be a function.
+    testString: assert(typeof farey === 'function');
+  - text: <code>farey(3)</code> should return an array
+    testString: assert(Array.isArray(farey(3)));
+  - text: <code>farey(3)</code> should return <code>["1/3","1/2","2/3"]</code>
+    testString: assert.deepEqual(farey(3), ["1/3","1/2","2/3"]);
+  - text: <code>farey(4)</code> should return <code>["1/4","1/3","1/2","2/4","2/3","3/4"]</code>
+    testString: assert.deepEqual(farey(4), ["1/4","1/3","1/2","2/4","2/3","3/4"]);
+  - text: <code>farey(5)</code> should return <code>["1/5","1/4","1/3","2/5","1/2","2/4","3/5","2/3","3/4","4/5"]</code>
+    testString: assert.deepEqual(farey(5), ["1/5","1/4","1/3","2/5","1/2","2/4","3/5","2/3","3/4","4/5"]);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function farey(n) {
+
+}
+```
+
+</div>
+
+
+
+</section>
+
+## Solution
+<section id='solution'>
+
+
+```js
+function farey(n){
+	let farSeq=[];
+	for(let den = 1; den <= n; den++){
+		for(let num = 1; num < den; num++){
+			farSeq.push({
+				str:num+"/"+den,
+				val:num/den});
+		}
+	}
+	farSeq.sort(function(a,b){
+		return a.val-b.val;
+	});
+	farSeq=farSeq.map(function(a){
+		return a.str;
+	});
+	return farSeq;
+}
+
+```
+
+</section>