2018-09-30 22:01:58 +00:00
|
|
|
|
---
|
|
|
|
|
id: 5900f4951000cf542c50ffa8
|
|
|
|
|
challengeType: 5
|
|
|
|
|
title: 'Problem 297: Zeckendorf Representation'
|
|
|
|
|
---
|
|
|
|
|
|
|
|
|
|
## Description
|
|
|
|
|
<section id='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.
|
|
|
|
|
</section>
|
|
|
|
|
|
|
|
|
|
## Instructions
|
|
|
|
|
<section id='instructions'>
|
|
|
|
|
|
|
|
|
|
</section>
|
|
|
|
|
|
|
|
|
|
## Tests
|
|
|
|
|
<section id='tests'>
|
|
|
|
|
|
|
|
|
|
```yml
|
2018-10-04 13:37:37 +00:00
|
|
|
|
tests:
|
|
|
|
|
- text: <code>euler297()</code> should return 2252639041804718000.
|
2018-10-20 18:02:47 +00:00
|
|
|
|
testString: assert.strictEqual(euler297(), 2252639041804718000, '<code>euler297()</code> should return 2252639041804718000.');
|
2018-09-30 22:01:58 +00:00
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
</section>
|
|
|
|
|
|
|
|
|
|
## Challenge Seed
|
|
|
|
|
<section id='challengeSeed'>
|
|
|
|
|
|
|
|
|
|
<div id='js-seed'>
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
function euler297() {
|
|
|
|
|
// Good luck!
|
|
|
|
|
return true;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
euler297();
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
</section>
|
|
|
|
|
|
|
|
|
|
## Solution
|
|
|
|
|
<section id='solution'>
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
// solution required
|
|
|
|
|
```
|
|
|
|
|
</section>
|