---
id: 5900f4ab1000cf542c50ffbe
challengeType: 5
title: 'Problem 319: Bounded Sequences'
---
## 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.
## Instructions
## Tests
```yml
tests:
- text: euler319() should return 268457129.
testString: assert.strictEqual(euler319(), 268457129);
```
## Challenge Seed
```js
function euler319() {
// Good luck!
return true;
}
euler319();
```