67 lines
968 B
Markdown
67 lines
968 B
Markdown
---
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id: 5900f53c1000cf542c51004e
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challengeType: 5
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title: 'Problem 463: A weird recurrence relation'
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forumTopicId: 302138
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---
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## Description
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<section id='description'>
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The function $f$ is defined for all positive integers as follows:
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$f(1)=1$
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$f(3)=3$
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$f(2n)=f(n)$
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$f(4n + 1)=2f(2n + 1) - f(n)$
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$f(4n + 3)=3f(2n + 1) - 2f(n)$
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The function $S(n)$ is defined as $\sum_{i=1}^{n}f(i)$.
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$S(8)=22$ and $S(100)=3604$.
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Find $S(3^{37})$. Give the last 9 digits of your answer.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler463()</code> should return 808981553.
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testString: assert.strictEqual(euler463(), 808981553);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler463() {
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// Good luck!
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return true;
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}
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euler463();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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