51 lines
977 B
Markdown
51 lines
977 B
Markdown
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---
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id: 5900f4ab1000cf542c50ffbe
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title: 'Problem 319: Bounded Sequences'
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challengeType: 5
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forumTopicId: 301975
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dashedName: problem-319-bounded-sequences
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---
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# --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: {2,4}, {2,5}, {2,6}, {2,7} and {2,8}. There are 293 such sequences of length 5; three examples are given below: {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. 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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# --hints--
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`euler319()` should return 268457129.
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```js
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assert.strictEqual(euler319(), 268457129);
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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 euler319() {
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return true;
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}
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euler319();
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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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