---
id: 5900f4951000cf542c50ffa8
title: 'Problem 297: Zeckendorf Representation'
challengeType: 5
forumTopicId: 301949
dashedName: problem-297-zeckendorf-representation
---

# --description--

Each new term in the Fibonacci sequence is generated by adding the previous two terms.

Starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.

Every positive integer can be uniquely written as a sum of nonconsecutive terms of the Fibonacci sequence. For example, 100 = 3 + 8 + 89. Such a sum is called the Zeckendorf representation of the number.

For any integer n>0, let z(n) be the number of terms in the Zeckendorf representation of n. Thus, z(5) = 1, z(14) = 2, z(100) = 3 etc. Also, for 0<n<106, ∑ z(n) = 7894453.

Find ∑ z(n) for 0<n<1017.

# --hints--

`euler297()` should return 2252639041804718000.

```js
assert.strictEqual(euler297(), 2252639041804718000);
```

# --seed--

## --seed-contents--

```js
function euler297() {

  return true;
}

euler297();
```

# --solutions--

```js
// solution required
```