2018-10-10 18:03:03 -04:00
|
|
|
|
---
|
|
|
|
|
|
id: 5900f4f81000cf542c51000b
|
|
|
|
|
|
challengeType: 5
|
|
|
|
|
|
title: 'Problem 396: Weak Goodstein sequence'
|
|
|
|
|
|
videoUrl: ''
|
|
|
|
|
|
localeTitle: 问题396：弱Goodstein序列
|
|
|
|
|
|
---
|
|
|
|
|
|
|
|
|
|
|
|
## Description
|
|
|
|
|
|
<section id="description">对于任何正整数n，第n个弱Goodstein序列{g1，g2，g3，...}定义为：g1 = n，对于k> 1，gk是通过在基k中写gk-1获得的，将其解释为a基数k + 1，减去1。 <p>当gk变为0时，序列终止。 </p><p>例如，第6个弱Goodstein序列是{6,11,17,25，...}：g1 = 6. g2 = 11，因为6 = 1102,1103 = 12，12 - 1 = 11. g3 = 17 11 = 1023,1024 = 18,18-1 = 17.g4 = 25，因为17 = 1014,1015 = 26,26-1 = 25。 </p><p>等等。 </p><p>可以证明，每个弱的Goodstein序列都会终止。 </p><p>设G（n）为第n个弱Goodstein序列中的非零元素的数量。可以证实G（2）= 3，G（4）= 21和G（6）= 381.还可以证实ΣG（n）= 2517，1≤n<8。 </p><p>找到ΣG（n）的最后9位数，1≤n<16。 </p></section>
|
|
|
|
|
|
|
|
|
|
|
|
## Instructions
|
|
|
|
|
|
<section id="instructions">
|
|
|
|
|
|
</section>
|
|
|
|
|
|
|
|
|
|
|
|
## Tests
|
|
|
|
|
|
<section id='tests'>
|
|
|
|
|
|
|
|
|
|
|
|
```yml
|
|
|
|
|
|
tests:
|
|
|
|
|
|
- text: <code>euler396()</code>应该返回173214653。
|
2020-02-18 01:40:55 +09:00
|
|
|
|
testString: assert.strictEqual(euler396(), 173214653);
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
</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>
|
