57 lines
931 B
Markdown
57 lines
931 B
Markdown
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---
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id: 5900f4c41000cf542c50ffd6
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title: 'Problem 343: Fractional Sequences'
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challengeType: 5
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forumTopicId: 302002
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dashedName: problem-343-fractional-sequences
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---
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# --description--
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For any positive integer k, a finite sequence ai of fractions xi/yi is defined by:
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a1 = 1/k and
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ai = (xi-1+1)/(yi-1-1) reduced to lowest terms for i>1.
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When ai reaches some integer n, the sequence stops. (That is, when yi=1.)
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Define f(k) = n.
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For example, for k = 20:
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1/20 → 2/19 → 3/18 = 1/6 → 2/5 → 3/4 → 4/3 → 5/2 → 6/1 = 6
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So f(20) = 6.
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Also f(1) = 1, f(2) = 2, f(3) = 1 and Σf(k3) = 118937 for 1 ≤ k ≤ 100.
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Find Σf(k3) for 1 ≤ k ≤ 2×106.
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# --hints--
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`euler343()` should return 269533451410884200.
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```js
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assert.strictEqual(euler343(), 269533451410884200);
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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 euler343() {
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return true;
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}
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euler343();
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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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