79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
80 lines
1.8 KiB
Markdown
80 lines
1.8 KiB
Markdown
---
|
||
id: 5900f4ed1000cf542c50fffe
|
||
challengeType: 5
|
||
title: 'Problem 384: Rudin-Shapiro sequence'
|
||
---
|
||
|
||
## Description
|
||
<section id='description'>
|
||
Define the sequence a(n) as the number of adjacent pairs of ones in the binary expansion of n (possibly overlapping).
|
||
E.g.: a(5) = a(1012) = 0, a(6) = a(1102) = 1, a(7) = a(1112) = 2
|
||
|
||
Define the sequence b(n) = (-1)a(n).
|
||
This sequence is called the Rudin-Shapiro sequence.
|
||
Also consider the summatory sequence of b(n): .
|
||
|
||
The first couple of values of these sequences are:
|
||
n 0 1 2 3 4 5 6 7
|
||
a(n) 0 0 0 1 0 0 1 2
|
||
b(n) 1 1 1 -1 1 1 -1 1
|
||
s(n) 1 2 3 2 3 4 3 4
|
||
|
||
The sequence s(n) has the remarkable property that all elements are positive and every positive integer k occurs exactly k times.
|
||
|
||
Define g(t,c), with 1 ≤ c ≤ t, as the index in s(n) for which t occurs for the c'th time in s(n).
|
||
E.g.: g(3,3) = 6, g(4,2) = 7 and g(54321,12345) = 1220847710.
|
||
|
||
Let F(n) be the fibonacci sequence defined by:
|
||
F(0)=F(1)=1 and
|
||
F(n)=F(n-1)+F(n-2) for n>1.
|
||
|
||
Define GF(t)=g(F(t),F(t-1)).
|
||
|
||
Find ΣGF(t) for 2≤t≤45.
|
||
</section>
|
||
|
||
## Instructions
|
||
<section id='instructions'>
|
||
|
||
</section>
|
||
|
||
## Tests
|
||
<section id='tests'>
|
||
|
||
```yml
|
||
tests:
|
||
- text: <code>euler384()</code> should return 3354706415856333000.
|
||
testString: assert.strictEqual(euler384(), 3354706415856333000, '<code>euler384()</code> should return 3354706415856333000.');
|
||
|
||
```
|
||
|
||
</section>
|
||
|
||
## Challenge Seed
|
||
<section id='challengeSeed'>
|
||
|
||
<div id='js-seed'>
|
||
|
||
```js
|
||
function euler384() {
|
||
// Good luck!
|
||
return true;
|
||
}
|
||
|
||
euler384();
|
||
```
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</section>
|
||
|
||
## Solution
|
||
<section id='solution'>
|
||
|
||
```js
|
||
// solution required
|
||
```
|
||
</section>
|