61 lines
1.2 KiB
Markdown
61 lines
1.2 KiB
Markdown
---
|
|
id: 5900f4141000cf542c50ff26
|
|
challengeType: 5
|
|
title: 'Problem 167: Investigating Ulam sequences'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
For two positive integers a and b, the Ulam sequence U(a,b) is defined by U(a,b)1 = a, U(a,b)2 = b and for k > 2,
|
|
U(a,b)k is the smallest integer greater than U(a,b)(k-1) which can be written in exactly one way as the sum of two distinct previous members of U(a,b).
|
|
For example, the sequence U(1,2) begins with
|
|
1, 2, 3 = 1 + 2, 4 = 1 + 3, 6 = 2 + 4, 8 = 2 + 6, 11 = 3 + 8;
|
|
5 does not belong to it because 5 = 1 + 4 = 2 + 3 has two representations as the sum of two previous members, likewise 7 = 1 + 6 = 3 + 4.
|
|
Find ∑U(2,2n+1)k for 2 ≤ n ≤10, where k = 1011.
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler167()</code> should return 3916160068885.
|
|
testString: 'assert.strictEqual(euler167(), 3916160068885, "<code>euler167()</code> should return 3916160068885.");'
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler167() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler167();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|