---
id: 5900f4a81000cf542c50ffbb
challengeType: 5
title: 'Problem 316: Numbers in decimal expansions'
---

## Description
<section id='description'>
Let p = p1 p2 p3 ... be an infinite sequence of random digits, selected from {0,1,2,3,4,5,6,7,8,9} with equal probability.
It can be seen that p corresponds to the real number 0.p1 p2 p3 .... 
It can also be seen that choosing a random real number from the interval [0,1) is equivalent to choosing an infinite sequence of random digits selected from {0,1,2,3,4,5,6,7,8,9} with equal probability.

For any positive integer n with d decimal digits, let k be the smallest index such that pk, pk+1, ...pk+d-1 are the decimal digits of n, in the same order.
Also, let g(n) be the expected value of k; it can be proven that g(n) is always finite and, interestingly, always an integer number.

For example, if n = 535, then
for p = 31415926535897...., we get k = 9
for p = 355287143650049560000490848764084685354..., we get k = 36
etc and we find that g(535) = 1008.

Given that , find 

Note:  represents the floor function.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler316()</code> should return 542934735751917760.
    testString: 'assert.strictEqual(euler316(), 542934735751917760, ''<code>euler316()</code> should return 542934735751917760.'');'

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler316() {
  // Good luck!
  return true;
}

euler316();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>