80 lines
1.5 KiB
Markdown
80 lines
1.5 KiB
Markdown
---
|
|
id: 5900f4f81000cf542c51000b
|
|
challengeType: 5
|
|
title: 'Problem 396: Weak Goodstein sequence'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
For any positive integer n, the nth weak Goodstein sequence {g1, g2, g3, ...} is defined as:
|
|
g1 = n
|
|
for k > 1, gk is obtained by writing gk-1 in base k, interpreting it as a base k + 1 number, and subtracting 1.
|
|
|
|
The sequence terminates when gk becomes 0.
|
|
|
|
|
|
For example, the 6th weak Goodstein sequence is {6, 11, 17, 25, ...}:
|
|
g1 = 6.
|
|
g2 = 11 since 6 = 1102, 1103 = 12, and 12 - 1 = 11.
|
|
g3 = 17 since 11 = 1023, 1024 = 18, and 18 - 1 = 17.
|
|
g4 = 25 since 17 = 1014, 1015 = 26, and 26 - 1 = 25.
|
|
|
|
and so on.
|
|
|
|
|
|
It can be shown that every weak Goodstein sequence terminates.
|
|
|
|
|
|
Let G(n) be the number of nonzero elements in the nth weak Goodstein sequence.
|
|
It can be verified that G(2) = 3, G(4) = 21 and G(6) = 381.
|
|
It can also be verified that ΣG(n) = 2517 for 1 ≤ n < 8.
|
|
|
|
|
|
Find the last 9 digits of ΣG(n) for 1 ≤ n < 16.
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler396()</code> should return 173214653.
|
|
testString: assert.strictEqual(euler396(), 173214653, '<code>euler396()</code> should return 173214653.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler396() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler396();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|