47 lines
1.0 KiB
Markdown
47 lines
1.0 KiB
Markdown
---
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id: 5900f4951000cf542c50ffa8
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title: 'Problem 297: Zeckendorf Representation'
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challengeType: 5
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forumTopicId: 301949
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dashedName: problem-297-zeckendorf-representation
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---
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# --description--
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Each new term in the Fibonacci sequence is generated by adding the previous two terms.
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Starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.
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Every positive integer can be uniquely written as a sum of nonconsecutive terms of the Fibonacci sequence. For example, 100 = 3 + 8 + 89. Such a sum is called the Zeckendorf representation of the number.
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For any integer n>0, let z(n) be the number of terms in the Zeckendorf representation of n. Thus, z(5) = 1, z(14) = 2, z(100) = 3 etc. Also, for 0<n<106, ∑ z(n) = 7894453.
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Find ∑ z(n) for 0<n<1017.
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# --hints--
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`euler297()` should return 2252639041804718000.
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```js
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assert.strictEqual(euler297(), 2252639041804718000);
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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 euler297() {
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return true;
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}
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euler297();
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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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