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