47 lines
931 B
Markdown
47 lines
931 B
Markdown
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---
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id: 5900f49d1000cf542c50ffaf
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title: 'Problem 304: Primonacci'
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challengeType: 5
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forumTopicId: 301958
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dashedName: problem-304-primonacci
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---
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# --description--
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For any positive integer $n$ the function $\text{next_prime}(n)$ returns the smallest prime $p$ such that $p > n$.
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The sequence $a(n)$ is defined by: $a(1) = \text{next_prime}({10}^{14})$ and $a(n) = \text{next_prime}(a(n - 1))$ for $n > 1$.
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The fibonacci sequence $f(n)$ is defined by: $f(0) = 0$, $f(1) = 1$ and $f(n) = f(n - 1) + f(n - 2)$ for $n > 1$.
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The sequence $b(n)$ is defined as $f(a(n))$.
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Find $\sum b(n)$ for $1≤n≤100\\,000$. Give your answer $\bmod 1\\,234\\,567\\,891\\,011$.
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# --hints--
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`primonacci()` should return `283988410192`.
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```js
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assert.strictEqual(primonacci(), 283988410192);
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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 primonacci() {
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return true;
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}
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primonacci();
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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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