2018-10-10 22:03:03 +00:00
|
|
|
|
---
|
|
|
|
|
id: 5900f5271000cf542c51003a
|
|
|
|
|
challengeType: 5
|
|
|
|
|
title: 'Problem 443: GCD sequence'
|
2019-08-28 13:26:13 +00:00
|
|
|
|
forumTopicId: 302115
|
2018-10-10 22:03:03 +00:00
|
|
|
|
localeTitle: 'Задача 443: последовательность GCD'
|
|
|
|
|
---
|
|
|
|
|
|
|
|
|
|
## Description
|
2019-08-28 13:26:13 +00:00
|
|
|
|
<section id='description'>
|
|
|
|
|
Let g(n) be a sequence defined as follows:
|
|
|
|
|
g(4) = 13,
|
|
|
|
|
g(n) = g(n-1) + gcd(n, g(n-1)) for n > 4.
|
|
|
|
|
|
|
|
|
|
The first few values are:
|
|
|
|
|
|
|
|
|
|
n 4567891011121314151617181920...
|
|
|
|
|
g(n) 1314161718272829303132333451545560...
|
|
|
|
|
|
|
|
|
|
<!-- TODO Use MathJax -->
|
|
|
|
|
|
|
|
|
|
You are given that g(1 000) = 2524 and g(1 000 000) = 2624152.
|
|
|
|
|
|
|
|
|
|
Find g(1015).
|
|
|
|
|
</section>
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
|
|
|
|
## Instructions
|
2019-08-28 13:26:13 +00:00
|
|
|
|
<section id='instructions'>
|
|
|
|
|
|
|
|
|
|
</section>
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
|
|
|
|
## Tests
|
|
|
|
|
<section id='tests'>
|
|
|
|
|
|
|
|
|
|
```yml
|
|
|
|
|
tests:
|
2019-08-28 13:26:13 +00:00
|
|
|
|
- text: <code>euler443()</code> should return 2744233049300770.
|
|
|
|
|
testString: assert.strictEqual(euler443(), 2744233049300770);
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
</section>
|
|
|
|
|
|
|
|
|
|
## Challenge Seed
|
|
|
|
|
<section id='challengeSeed'>
|
|
|
|
|
|
|
|
|
|
<div id='js-seed'>
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
function euler443() {
|
|
|
|
|
// Good luck!
|
|
|
|
|
return true;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
euler443();
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
</section>
|
|
|
|
|
|
|
|
|
|
## Solution
|
|
|
|
|
<section id='solution'>
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
// solution required
|
|
|
|
|
```
|
2019-08-28 13:26:13 +00:00
|
|
|
|
|
2018-10-10 22:03:03 +00:00
|
|
|
|
</section>
|