---
title: Fractran
id: 5a7dad05be01840e1778a0d1
challengeType: 3
---

## Description
<section id='description'>
<div class="rosetta"><p class="rosetta__paragraph"><span class="rosetta__text--bold"><a class="rosetta__link--wiki" href="https://en.wikipedia.org/wiki/FRACTRAN" title="wp: FRACTRAN">FRACTRAN</a></span> is a Turing-complete esoteric programming language invented by the mathematician <a class="rosetta__link--wiki" href="https://en.wikipedia.org/wiki/John Horton Conway" title="wp: John Horton Conway">John Horton Conway</a>.</p><br/><p class="rosetta__paragraph">A FRACTRAN program is an ordered list of positive fractions $P = (f_1, f_2, \ldots, f_m)$, together with an initial positive integer input $n$.</p>
<br/><p class="rosetta__paragraph">The program is run by updating the integer $n$ as follows:</p><br/><ul class="rosetta__unordered-list"><li class="rosetta__list-item--unordered">for the first fraction, $f_i$, in the list for which $nf_i$ is an integer, replace $n$ with $nf_i$ ;</li>
<li class="rosetta__list-item--unordered">repeat this rule until no fraction in the list produces an integer when multiplied by $n$, then halt.</li></ul>
<br>
<p class="rosetta__paragraph">Conway gave a program for primes in FRACTRAN:</p><br/><p class="rosetta__paragraph"><span class="rosetta__text--indented"> $17/91$, $78/85$, $19/51$, $23/38$, $29/33$, $77/29$, $95/23$, $77/19$, $1/17$, $11/13$, $13/11$, $15/14$, $15/2$, $55/1$</span></p><br/><p class="rosetta__paragraph">Starting with $n=2$, this FRACTRAN program will change $n$ to $15=2\times (15/2)$, then $825=15\times (55/1)$, generating the following sequence of integers:</p><br/><p class="rosetta__paragraph"><span class="rosetta__text--indented"> $2$, $15$, $825$, $725$, $1925$, $2275$, $425$, $390$, $330$, $290$, $770$, $\ldots$</span></p><br/><p class="rosetta__paragraph">After 2, this sequence contains the following powers of 2:</p><br/><p class="rosetta__paragraph"><span class="rosetta__text--indented">$2^2=4$, $2^3=8$, $2^5=32$, $2^7=128$, $2^{11}=2048$, $2^{13}=8192$, $2^{17}=131072$, $2^{19}=524288$, $\ldots$</span></p><br/><p class="rosetta__paragraph">which are the prime powers of 2.</p>
<br/><dl class="rosetta__description-list"><dt class="rosetta__description-title">Task:</dt></dl>
<p class="rosetta__paragraph">Write a function that takes a fractran program as a string parameter and returns the first 10 numbers of the program as an array. If the result does not have 10 numbers then return the numbers as is.</p></div>
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>fractran</code> should be a function.
    testString: 'assert(typeof fractran=="function","<code>fractran</code> should be a function.");'
  - text: '<code>fractran(""+tests[0]+"")</code> should return an array.'
    testString: 'assert(Array.isArray(fractran(tests[0])),"<code>fractran(""+tests[0]+"")</code> should return an array.");'
  - text: '<code>fractran(""+tests[0]+"")</code> should return <code>"+JSON.stringify(results[0])+"</code>.'
    testString: 'assert.deepEqual(fractran(tests[0]),results[0],"<code>fractran(""+tests[0]+"")</code> should return <code>"+JSON.stringify(results[0])+"</code>.");'
  - text: '<code>fractran(""+tests[1]+"")</code> should return <code>"+JSON.stringify(results[1])+"</code>.'
    testString: 'assert.deepEqual(fractran(tests[1]),results[1],"<code>fractran(""+tests[1]+"")</code> should return <code>"+JSON.stringify(results[1])+"</code>.");'
  - text: '<code>fractran(""+tests[2]+"")</code> should return <code>"+JSON.stringify(results[2])+"</code>.'
    testString: 'assert.deepEqual(fractran(tests[2]),results[2],"<code>fractran(""+tests[2]+"")</code> should return <code>"+JSON.stringify(results[2])+"</code>.");'
  - text: '<code>fractran(""+tests[3]+"")</code> should return <code>"+JSON.stringify(results[3])+"</code>.'
    testString: 'assert.deepEqual(fractran(tests[3]),results[3],"<code>fractran(""+tests[3]+"")</code> should return <code>"+JSON.stringify(results[3])+"</code>.");'
  - text: '<code>fractran(""+tests[4]+"")</code> should return <code>"+JSON.stringify(results[4])+"</code>.'
    testString: 'assert.deepEqual(fractran(tests[4]),results[4],"<code>fractran(""+tests[4]+"")</code> should return <code>"+JSON.stringify(results[4])+"</code>.");'

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function fractran (progStr) {
  // Good luck!
}
```

</div>


### After Test
<div id='js-teardown'>

```js
console.info('after the test');
```

</div>

</section>

## Solution
<section id='solution'>


```js
function fractran(progStr){
  var num = new Array();
  var den = new Array();
  var val ;
  var out="";
  function compile(prog){
    var regex = /\s*(\d*)\s*\/\s*(\d*)\s*(.*)/m;
    while(regex.test(prog)){
      num.push(regex.exec(prog)[1]);
      den.push(regex.exec(prog)[2]);
      prog = regex.exec(prog)[3];
    }
  }

  function step(val){
    var i=0;
    while(i<den.length && val%den[i] != 0) i++;
    return num[i]*val/den[i];
  }

  var seq=[]

  function exec(val){
    var i = 0;
    while(val && i<limit){
      seq.push(val)
      val = step(val);
      i ++;
    }
  }

  // Main
  compile(progStr);
  var limit = 10;
  exec(2);
  return seq;
}

```

</section>