---
id: 5900f4d51000cf542c50ffe8
challengeType: 5
title: 'Problem 361: Subsequence of Thue-Morse sequence'
forumTopicId: 302022
---

## Description
<section id='description'>
The Thue-Morse sequence {Tn} is a binary sequence satisfying:
T0 = 0
T2n = Tn
T2n+1 = 1 - Tn

The first several terms of {Tn} are given as follows:
01101001100101101001011001101001....



We define {An} as the sorted sequence of integers such that the binary expression of each element appears as a subsequence in {Tn}.
For example, the decimal number 18 is expressed as 10010 in binary. 10010 appears in {Tn} (T8 to T12), so 18 is an element of {An}.
The decimal number 14 is expressed as 1110 in binary. 1110 never appears in {Tn}, so 14 is not an element of {An}.



The first several terms of An are given as follows:
n0123456789101112…An012345691011121318…



We can also verify that A100 = 3251 and A1000 = 80852364498.



Find the last 9 digits of .
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler361()</code> should return 178476944.
    testString: assert.strictEqual(euler361(), 178476944);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler361() {

  return true;
}

euler361();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>