53 lines
995 B
Markdown
53 lines
995 B
Markdown
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---
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id: 5900f4be1000cf542c50ffd0
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title: 'Problem 337: Totient Stairstep Sequences'
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challengeType: 5
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forumTopicId: 301995
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dashedName: problem-337-totient-stairstep-sequences
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---
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# --description--
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Let $\\{a_1, a_2, \ldots, a_n\\}$ be an integer sequence of length $n$ such that:
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- $a_1 = 6$
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- for all $1 ≤ i < n$ : $φ(a_i) < φ(a_{i + 1}) < a_i < a_{i + 1}$
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$φ$ denotes Euler's totient function.
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Let $S(N)$ be the number of such sequences with $a_n ≤ N$.
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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 $S(100) = 482\\,073\\,668$ and $S(10\\,000)\bmod {10}^8 = 73\\,808\\,307$.
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Find $S(20\\,000\\,000)\bmod {10}^8$.
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# --hints--
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`totientStairstepSequences()` should return `85068035`.
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```js
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assert.strictEqual(totientStairstepSequences(), 85068035);
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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 totientStairstepSequences() {
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return true;
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}
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totientStairstepSequences();
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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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