---
id: 5900f5271000cf542c510039
title: 'Problem 442: Eleven-free integers'
challengeType: 5
forumTopicId: 302114
dashedName: problem-442-eleven-free-integers
---

# --description--

An integer is called eleven-free if its decimal expansion does not contain any substring representing a power of 11 except 1.

For example, 2404 and 13431 are eleven-free, while 911 and 4121331 are not.

Let $E(n)$ be the $n$th positive eleven-free integer. For example, $E(3) = 3$, $E(200) = 213$ and $E(500\\,000) = 531\\,563$.

Find $E({10}^{18})$.

# --hints--

`elevenFreeIntegers()` should return `1295552661530920200`.

```js
assert.strictEqual(elevenFreeIntegers(), 1295552661530920200);
```

# --seed--

## --seed-contents--

```js
function elevenFreeIntegers() {

  return true;
}

elevenFreeIntegers();
```

# --solutions--

```js
// solution required
```