65 lines
1.6 KiB
Markdown
65 lines
1.6 KiB
Markdown
---
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id: 5900f41c1000cf542c50ff2e
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challengeType: 5
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title: 'Problem 175: Fractions involving the number of different ways a number can be expressed as a sum of powers of 2'
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---
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## Description
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<section id='description'>
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Define f(0)=1 and f(n) to be the number of ways to write n as a sum of powers of 2 where no power occurs more than twice.
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For example, f(10)=5 since there are five different ways to express 10:10 = 8+2 = 8+1+1 = 4+4+2 = 4+2+2+1+1 = 4+4+1+1
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It can be shown that for every fraction p/q (p>0, q>0) there exists at least one integer n such that f(n)/f(n-1)=p/q.
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For instance, the smallest n for which f(n)/f(n-1)=13/17 is 241.
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The binary expansion of 241 is 11110001.
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Reading this binary number from the most significant bit to the least significant bit there are 4 one's, 3 zeroes and 1 one. We shall call the string 4,3,1 the Shortened Binary Expansion of 241.
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Find the Shortened Binary Expansion of the smallest n for which f(n)/f(n-1)=123456789/987654321.
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Give your answer as comma separated integers, without any whitespaces.
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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>euler175()</code> should return 1, 13717420, 8.
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testString: assert.strictEqual(euler175(), 1, 13717420, 8, '<code>euler175()</code> should return 1, 13717420, 8.');
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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 euler175() {
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// Good luck!
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return true;
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}
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euler175();
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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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