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---
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
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tests:
- text: < code > euler167()</ code > should return 3916160068885.
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testString: 'assert.strictEqual(euler167(), 3916160068885, "< code > euler167()< / code > should return 3916160068885.");'
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```
< / 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 >