---
id: 5a23c84252665b21eecc8028
title: Stern-Brocot sequence
challengeType: 5
forumTopicId: 302324
dashedName: stern-brocot-sequence
---

# --description--

For this task, the Stern-Brocot sequence is to be generated by an algorithm similar to that employed in generating the [Fibonacci sequence](https://rosettacode.org/wiki/Fibonacci sequence).

<ol>
  <li>The first and second members of the sequence are both 1:</li>
    <ul><li>1, 1</li></ul>
  <li>Start by considering the second member of the sequence</li>
  <li>Sum the considered member of the sequence and its precedent, (1 + 1) = 2, and append it to the end of the
    sequence:</li>
    <ul><li>1, 1, 2</li></ul>
  <li>Append the considered member of the sequence to the end of the sequence:</li>
    <ul><li>1, 1, 2, 1</li></ul>
  <li>Consider the next member of the series, (the third member i.e. 2)</li>
  <li>GOTO 3 </li>
    <ul>
      <li></li>
      <li> ─── Expanding another loop we get: ───</li>
      <li></li>
    </ul>
  <li>Sum the considered member of the sequence and its precedent, (2 + 1) = 3, and append it to the end of the
    sequence:</li>
    <ul><li>1, 1, 2, 1, 3</li></ul>
  <li>Append the considered member of the sequence to the end of the sequence:</li>
    <ul><li>1, 1, 2, 1, 3, 2</li></ul>
  <li>Consider the next member of the series, (the fourth member i.e. 1)</li>
</ol>

# --instructions--

Create a function that returns the position in the Stern-Brocot sequence at which $ n $ is first encountered, where the sequence is generated with the method outlined above. Note that this sequence uses 1 based indexing.

# --hints--

`sternBrocot` should be a function.

```js
assert(typeof sternBrocot == 'function');
```

`sternBrocot(2)` should return a number.

```js
assert(typeof sternBrocot(2) == 'number');
```

`sternBrocot(2)` should return `3`.

```js
assert.equal(sternBrocot(2), 3);
```

`sternBrocot(3)` should return `5`.

```js
assert.equal(sternBrocot(3), 5);
```

`sternBrocot(5)` should return `11`.

```js
assert.equal(sternBrocot(5), 11);
```

`sternBrocot(7)` should return `19`.

```js
assert.equal(sternBrocot(7), 19);
```

`sternBrocot(10)` should return `39`.

```js
assert.equal(sternBrocot(10), 39);
```

# --seed--

## --seed-contents--

```js
function sternBrocot(num) {

}
```

# --solutions--

```js
function sternBrocot(num) {
  function f(n) {
    return n < 2
      ? n
      : n & 1
      ? f(Math.floor(n / 2)) + f(Math.floor(n / 2 + 1))
      : f(Math.floor(n / 2));
  }

  function gcd(a, b) {
    return a ? (a < b ? gcd(b % a, a) : gcd(a % b, b)) : b;
  }
  var n;
  for (n = 1; f(n) != num; n++);
  return n;
}
```
