---
id: 5900f49d1000cf542c50ffb0
title: 'Problem 305: Reflexive Position'
challengeType: 5
forumTopicId: 301959
dashedName: problem-305-reflexive-position
---

# --description--

Let's call S the (infinite) string that is made by concatenating the consecutive positive integers (starting from 1) written down in base 10.

Thus, S = 1234567891011121314151617181920212223242...

It's easy to see that any number will show up an infinite number of times in S.

Let's call f(n) the starting position of the nth occurrence of n in S. For example, f(1)=1, f(5)=81, f(12)=271 and f(7780)=111111365.

Find ∑f(3k) for 1≤k≤13.

# --hints--

`euler305()` should return 18174995535140.

```js
assert.strictEqual(euler305(), 18174995535140);
```

# --seed--

## --seed-contents--

```js
function euler305() {

  return true;
}

euler305();
```

# --solutions--

```js
// solution required
```