55 lines
1.2 KiB
Markdown
55 lines
1.2 KiB
Markdown
---
|
|
id: 5900f4d51000cf542c50ffe8
|
|
title: 'Problem 361: Subsequence of Thue-Morse sequence'
|
|
challengeType: 5
|
|
forumTopicId: 302022
|
|
dashedName: problem-361-subsequence-of-thue-morse-sequence
|
|
---
|
|
|
|
# --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 .
|
|
|
|
# --hints--
|
|
|
|
`euler361()` should return 178476944.
|
|
|
|
```js
|
|
assert.strictEqual(euler361(), 178476944);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function euler361() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler361();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|