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---
id: 5a23c84252665b21eecc8028
title: Stern-Brocot sequence
challengeType: 5
forumTopicId: 302324
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dashedName: stern-brocot-sequence
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---
# --description--
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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 ).
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< 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--
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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.
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# --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;
}
```