32dbe23f5e
* fix: clean-up Project Euler 301-320 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
49 lines
1.0 KiB
Markdown
49 lines
1.0 KiB
Markdown
---
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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 $x_1, x_2, \ldots, x_n$ be a sequence of length $n$ such that:
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- $x_1 = 2$
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- for all $1 < i ≤ n : x_{i - 1} < x_i$
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- for all $i$ and $j$ with $1 ≤ i, j ≤ n : {(x_i)}^j < {(x_j + 1)}^i$
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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 $t({10}^{10})$ and give your answer modulo $10^9$.
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# --hints--
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`boundedSequences()` should return `268457129`.
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```js
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assert.strictEqual(boundedSequences(), 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 boundedSequences() {
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return true;
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}
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boundedSequences();
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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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