2018-09-30 22:01:58 +00:00
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---
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id: 5900f46e1000cf542c50ff81
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title: 'Problem 258: A lagged Fibonacci sequence'
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2020-11-27 18:02:05 +00:00
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challengeType: 5
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2019-08-05 16:17:33 +00:00
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forumTopicId: 301906
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2021-01-13 02:31:00 +00:00
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dashedName: problem-258-a-lagged-fibonacci-sequence
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2018-09-30 22:01:58 +00:00
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---
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2020-11-27 18:02:05 +00:00
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# --description--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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A sequence is defined as:
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2018-09-30 22:01:58 +00:00
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2021-07-16 10:21:45 +00:00
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- $g_k = 1$, for $0 ≤ k ≤ 1999$
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- $g_k = g_{k - 2000} + g_{k - 1999}$, for $k ≥ 2000$.
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Find $g_k$ mod 20092010 for $k = {10}^{18}$.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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# --hints--
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2018-09-30 22:01:58 +00:00
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2021-07-16 10:21:45 +00:00
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`laggedFibonacciSequence()` should return `12747994`.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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```js
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2021-07-16 10:21:45 +00:00
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assert.strictEqual(laggedFibonacciSequence(), 12747994);
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --seed--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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## --seed-contents--
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2018-09-30 22:01:58 +00:00
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```js
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2021-07-16 10:21:45 +00:00
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function laggedFibonacciSequence() {
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2020-09-15 16:57:40 +00:00
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2018-09-30 22:01:58 +00:00
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return true;
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}
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2021-07-16 10:21:45 +00:00
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laggedFibonacciSequence();
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --solutions--
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2018-09-30 22:01:58 +00:00
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```js
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// solution required
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```
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