71 lines
1.2 KiB
Markdown
71 lines
1.2 KiB
Markdown
|
---
|
||
|
id: 5900f4ab1000cf542c50ffbe
|
||
|
challengeType: 5
|
||
|
title: 'Problem 319: Bounded Sequences'
|
||
|
---
|
||
|
|
||
|
## Description
|
||
|
<section id='description'>
|
||
|
Let x1, x2,..., xn be a sequence of length n such that:
|
||
|
x1 = 2
|
||
|
for all 1 < i ≤ n : xi-1 < xi
|
||
|
for all i and j with 1 ≤ i, j ≤ n : (xi) j < (xj + 1)i
|
||
|
|
||
|
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}.
|
||
|
|
||
|
|
||
|
Let t(n) denote the number of such sequences of length n.
|
||
|
You are given that t(10) = 86195 and t(20) = 5227991891.
|
||
|
|
||
|
|
||
|
Find t(1010) and give your answer modulo 109.
|
||
|
</section>
|
||
|
|
||
|
## Instructions
|
||
|
<section id='instructions'>
|
||
|
|
||
|
</section>
|
||
|
|
||
|
## Tests
|
||
|
<section id='tests'>
|
||
|
|
||
|
```yml
|
||
|
tests:
|
||
|
- text: <code>euler319()</code> should return 268457129.
|
||
|
testString: 'assert.strictEqual(euler319(), 268457129, ''<code>euler319()</code> should return 268457129.'');'
|
||
|
|
||
|
```
|
||
|
|
||
|
</section>
|
||
|
|
||
|
## Challenge Seed
|
||
|
<section id='challengeSeed'>
|
||
|
|
||
|
<div id='js-seed'>
|
||
|
|
||
|
```js
|
||
|
function euler319() {
|
||
|
// Good luck!
|
||
|
return true;
|
||
|
}
|
||
|
|
||
|
euler319();
|
||
|
```
|
||
|
|
||
|
</div>
|
||
|
|
||
|
|
||
|
|
||
|
</section>
|
||
|
|
||
|
## Solution
|
||
|
<section id='solution'>
|
||
|
|
||
|
```js
|
||
|
// solution required
|
||
|
```
|
||
|
</section>
|