freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/hailstone-sequence.english.md

---
title: Hailstone sequence
id: 595608ff8bcd7a50bd490181
challengeType: 5
---

## Description
<section id='description'>
<p>The Hailstone sequence of numbers can be generated from a starting positive integer,  n  by:</p>
 If  n  is   1   then the sequence ends.
 If  n  is  even then the next  n  of the sequence <code> = n/2 </code>
 If  n  is  odd   then the next  n  of the sequence <code> = (3 * n) + 1 </code><p>The (unproven) <a href="https://en.wikipedia.org/wiki/Collatz conjecture" title="wp: Collatz conjecture">Collatz conjecture</a> is that the hailstone sequence for any starting number always terminates.</p>
<p>The hailstone sequence is also known as hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as the Collatz sequence.</p>
Task:
Create a routine to generate the hailstone sequence for a number.
Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with <code>27, 82, 41, 124</code> and ending with <code>8, 4, 2, 1</code>
Show the number less than 100,000 which has the longest hailstone sequence together with that sequence's length.   (But don't show the actual sequence!)See also:
 <a href="http://xkcd.com/710" title="link: http://xkcd.com/710">xkcd</a> (humourous).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>hailstoneSequence</code> is a function.
    testString: assert(typeof hailstoneSequence === 'function', '<code>hailstoneSequence</code> is a function.');
  - text: <code>hailstoneSequence()</code> should return <code>[[27,82,41,124,8,4,2,1], [351, 77031]]</code>
    testString: assert.deepEqual(hailstoneSequence(), res, '<code>hailstoneSequence()</code> should return <code>[[27,82,41,124,8,4,2,1], [351, 77031]]</code>');

```

</section>

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

<div id='js-seed'>

```js
// noprotect
function hailstoneSequence () {
  const res = [];
  // Good luck!

  return res;
}
```

</div>


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

```js
const res = [[27, 82, 41, 124, 8, 4, 2, 1], [351, 77031]];
```

</div>

</section>

## Solution
<section id='solution'>


```js
// noprotect
function hailstoneSequence () {
  const res = [];

  function hailstone(n) {
    const seq = [n];
    while (n > 1) {
      n = n % 2 ? 3 * n + 1 : n / 2;
      seq.push(n);
    }
    return seq;
  }

  const h = hailstone(27);
  const hLen = h.length;
  res.push([...h.slice(0, 4), ...h.slice(hLen - 4, hLen)]);

  let n = 0;
  let max = 0;
  for (let i = 100000; --i;) {
    const seq = hailstone(i);
    const sLen = seq.length;

    if (sLen > max) {
      n = i;
      max = sLen;
    }
  }
  res.push([max, n]);

  return res;
}

```

</section>