73 lines
1.2 KiB
Markdown
73 lines
1.2 KiB
Markdown
---
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id: 5900f4ab1000cf542c50ffbe
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challengeType: 5
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title: 'Problem 319: Bounded Sequences'
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forumTopicId: 301975
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---
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## Description
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<section id='description'>
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Let x1, x2,..., xn be a sequence of length n such that:
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x1 = 2
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for all 1 < i ≤ n : xi-1 < xi
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for all i and j with 1 ≤ i, j ≤ n : (xi) j < (xj + 1)i
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There are only five such sequences of length 2, namely:
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{2,4}, {2,5}, {2,6}, {2,7} and {2,8}.
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There are 293 such sequences of length 5; three examples are given below:
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{2,5,11,25,55}, {2,6,14,36,88}, {2,8,22,64,181}.
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Let t(n) denote the number of such sequences of length n.
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You are given that t(10) = 86195 and t(20) = 5227991891.
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Find t(1010) and give your answer modulo 109.
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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>euler319()</code> should return 268457129.
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testString: assert.strictEqual(euler319(), 268457129);
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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 euler319() {
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return true;
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}
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euler319();
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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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