47 lines
881 B
Markdown
47 lines
881 B
Markdown
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---
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id: 5900f53c1000cf542c51004e
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title: 'Problem 463: A weird recurrence relation'
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challengeType: 5
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forumTopicId: 302138
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dashedName: problem-463-a-weird-recurrence-relation
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---
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# --description--
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The function $f$ is defined for all positive integers as follows:
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$$\begin{align} & f(1) = 1 \\\\ & f(3) = 3 \\\\ & f(2n) = f(n) \\\\ & f(4n + 1) = 2f(2n + 1) - f(n) \\\\ & f(4n + 3) = 3f(2n + 1) - 2f(n) \end{align}$$
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The function $S(n)$ is defined as $\sum_{i=1}^{n} f(i)$.
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$S(8) = 22$ and $S(100) = 3604$.
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Find $S(3^{37})$. Give the last 9 digits of your answer.
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# --hints--
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`weirdRecurrenceRelation()` should return `808981553`.
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```js
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assert.strictEqual(weirdRecurrenceRelation(), 808981553);
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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 weirdRecurrenceRelation() {
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return true;
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}
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weirdRecurrenceRelation();
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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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