c18554dd44
* fix: clean-up Project Euler 341-360 * fix: improve wording Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
56 lines
1.2 KiB
Markdown
56 lines
1.2 KiB
Markdown
---
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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 $a_i$ of fractions $\frac{x_i}{y_i}$ is defined by:
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- $a_1 = \displaystyle\frac{1}{k}$ and
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- $a_i = \displaystyle\frac{(x_{i - 1} + 1)}{(y_{i - 1} - 1)}$ reduced to lowest terms for $i > 1$.
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When $a_i$ reaches some integer $n$, the sequence stops. (That is, when $y_i = 1$.)
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Define $f(k) = n$.
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For example, for $k = 20$:
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$$\frac{1}{20} → \frac{2}{19} → \frac{3}{18} = \frac{1}{6} → \frac{2}{5} → \frac{3}{4} → \frac{4}{3} → \frac{5}{2} → \frac{6}{1} = 6$$
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So $f(20) = 6$.
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Also $f(1) = 1$, $f(2) = 2$, $f(3) = 1$ and $\sum f(k^3) = 118\\,937$ for $1 ≤ k ≤ 100$.
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Find $\sum f(k^3)$ for $1 ≤ k ≤ 2 × {10}^6$.
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# --hints--
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`fractionalSequences()` should return `269533451410884200`.
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```js
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assert.strictEqual(fractionalSequences(), 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 fractionalSequences() {
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return true;
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}
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fractionalSequences();
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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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