79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
75 lines
1.2 KiB
Markdown
75 lines
1.2 KiB
Markdown
---
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id: 5900f4421000cf542c50ff55
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challengeType: 5
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title: 'Problem 214: Totient Chains'
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---
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## Description
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<section id='description'>
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Let φ be Euler's totient function, i.e. for a natural number n,
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φ(n) is the number of k, 1 ≤ k ≤ n, for which gcd(k,n) = 1.
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By iterating φ, each positive integer generates a decreasing chain of numbers ending in 1.
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E.g. if we start with 5 the sequence 5,4,2,1 is generated.
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Here is a listing of all chains with length 4:
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5,4,2,1
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7,6,2,1
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8,4,2,1
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9,6,2,1
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10,4,2,1
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12,4,2,1
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14,6,2,1
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18,6,2,1
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Only two of these chains start with a prime, their sum is 12.
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What is the sum of all primes less than 40000000 which generate a chain of length 25?
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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>euler214()</code> should return 1677366278943.
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testString: assert.strictEqual(euler214(), 1677366278943, '<code>euler214()</code> should return 1677366278943.');
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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 euler214() {
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// Good luck!
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return true;
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}
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euler214();
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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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