67 lines
1.0 KiB
Markdown
67 lines
1.0 KiB
Markdown
---
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id: 5900f4be1000cf542c50ffd0
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challengeType: 5
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title: 'Problem 337: Totient Stairstep Sequences'
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forumTopicId: 301995
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---
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## Description
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<section id='description'>
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Let {a1, a2,..., an} be an integer sequence of length n such that:
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a1 = 6
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for all 1 ≤ i < n : φ(ai) < φ(ai+1) < ai < ai+11
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Let S(N) be the number of such sequences with an ≤ N.
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For example, S(10) = 4: {6}, {6, 8}, {6, 8, 9} and {6, 10}.
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We can verify that S(100) = 482073668 and S(10 000) mod 108 = 73808307.
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Find S(20 000 000) mod 108.
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1 φ denotes Euler's totient function.
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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>euler337()</code> should return 85068035.
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testString: assert.strictEqual(euler337(), 85068035);
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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 euler337() {
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return true;
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}
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euler337();
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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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