2018-10-10 22:03:03 +00:00
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---
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id: 5900f3f51000cf542c50ff08
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2020-12-16 07:37:30 +00:00
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title: 问题137:斐波那契金块
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2018-10-10 22:03:03 +00:00
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challengeType: 5
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videoUrl: ''
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---
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2020-12-16 07:37:30 +00:00
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# --description--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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考虑无穷多项式系列AF(x)= xF1 + x2F2 + x3F3 + ...,其中Fk是斐波纳契数列中的第k项:1,1,2,3,5,8,...;也就是说,Fk = Fk-1 + Fk-2,F1 = 1且F2 = 1.对于这个问题,我们将对x的值感兴趣,其中AF(x)是正整数。令人惊讶的是AF(1/2)=(1/2).1 +(1/2)2.1 +(1/2)3.2 +(1/2)4.3 +(1/2)5.5 + ......
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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= 1/2 + 1/4 + 2/8 + 3/16 + 5/32 + ......
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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= 2前五个自然数的x的相应值如下所示。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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xAF(x)√2-111/ 22(√13-2)/ 33(√89-5)/ 84(√34-3)/ 55
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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如果x是理性的,我们将AF(x)称为金块,因为它们变得越来越稀少;例如,第10个金块是74049690.找到第15个金块。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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# --hints--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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`euler137()`应该返回1120149658760。
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2018-10-10 22:03:03 +00:00
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```js
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2020-12-16 07:37:30 +00:00
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assert.strictEqual(euler137(), 1120149658760);
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2018-10-10 22:03:03 +00:00
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```
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2020-12-16 07:37:30 +00:00
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# --solutions--
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2020-08-13 15:24:35 +00:00
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