eef1805fe6
* fix: clean-up Project Euler 201-220 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
56 lines
1.1 KiB
Markdown
56 lines
1.1 KiB
Markdown
---
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id: 5900f4421000cf542c50ff55
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title: 'Problem 214: Totient Chains'
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challengeType: 5
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forumTopicId: 301856
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dashedName: problem-214-totient-chains
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---
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# --description--
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Let $φ$ be Euler's totient function, i.e. for a natural number $n$, $φ(n)$ 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. E.g. if we start with 5 the sequence 5,4,2,1 is generated. Here is a listing of all chains with length 4:
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$$\begin{align}
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5,4,2,1 & \\\\
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7,6,2,1 & \\\\
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8,4,2,1 & \\\\
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9,6,2,1 & \\\\
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10,4,2,1 & \\\\
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12,4,2,1 & \\\\
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14,6,2,1 & \\\\
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18,6,2,1 &
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\end{align}$$
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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 $40\\,000\\,000$ which generate a chain of length 25?
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# --hints--
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`totientChains()` should return `1677366278943`.
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```js
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assert.strictEqual(totientChains(), 1677366278943);
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```
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# --seed--
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## --seed-contents--
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```js
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function totientChains() {
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return true;
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}
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totientChains();
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```
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# --solutions--
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```js
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// solution required
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```
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