81 lines
1.4 KiB
Markdown
81 lines
1.4 KiB
Markdown
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---
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id: 5900f4d51000cf542c50ffe8
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challengeType: 5
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title: 'Problem 361: Subsequence of Thue-Morse sequence'
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---
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## Description
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<section id='description'>
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The Thue-Morse sequence {Tn} is a binary sequence satisfying:
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T0 = 0
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T2n = Tn
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T2n+1 = 1 - Tn
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The first several terms of {Tn} are given as follows:
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01101001100101101001011001101001....
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We define {An} as the sorted sequence of integers such that the binary expression of each element appears as a subsequence in {Tn}.
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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}.
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The decimal number 14 is expressed as 1110 in binary. 1110 never appears in {Tn}, so 14 is not an element of {An}.
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The first several terms of An are given as follows:
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n0123456789101112…An012345691011121318…
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We can also verify that A100 = 3251 and A1000 = 80852364498.
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Find the last 9 digits of .
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler361()</code> should return 178476944.
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testString: 'assert.strictEqual(euler361(), 178476944, ''<code>euler361()</code> should return 178476944.'');'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler361() {
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// Good luck!
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return true;
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}
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euler361();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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