79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
73 lines
1.8 KiB
Markdown
73 lines
1.8 KiB
Markdown
---
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id: 5900f5461000cf542c510058
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challengeType: 5
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title: 'Problem 473: Phigital number base'
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---
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## Description
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<section id='description'>
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Let $\varphi$ be the golden ratio: $\varphi=\frac{1+\sqrt{5}}{2}.$
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Remarkably it is possible to write every positive integer as a sum of powers of $\varphi$ even if we require that every power of $\varphi$ is used at most once in this sum.
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Even then this representation is not unique.
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We can make it unique by requiring that no powers with consecutive exponents are used and that the representation is finite.
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E.g:
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$2=\varphi+\varphi^{-2}$ and $3=\varphi^{2}+\varphi^{-2}$
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To represent this sum of powers of $\varphi$ we use a string of 0's and 1's with a point to indicate where the negative exponents start.
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We call this the representation in the phigital numberbase.
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So $1=1_{\varphi}$, $2=10.01_{\varphi}$, $3=100.01_{\varphi}$ and $14=100100.001001_{\varphi}$.
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The strings representing 1, 2 and 14 in the phigital number base are palindromic, while the string representing 3 is not. (the phigital point is not the middle character).
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The sum of the positive integers not exceeding 1000 whose phigital representation is palindromic is 4345.
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Find the sum of the positive integers not exceeding $10^{10}$ whose phigital representation is palindromic.
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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>euler473()</code> should return 35856681704365.
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testString: assert.strictEqual(euler473(), 35856681704365, '<code>euler473()</code> should return 35856681704365.');
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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 euler473() {
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// Good luck!
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return true;
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}
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euler473();
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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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