2018-10-10 22:03:03 +00:00
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---
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id: 5900f4b71000cf542c50ffc9
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2020-12-16 07:37:30 +00:00
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title: 问题330:欧拉数
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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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为所有整数n定义了无限的实数序列a(n),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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例如,a(0)= 11! + 12! + 13! + ... = e - 1 a(1)= e - 11! + 12! + 13! + ... = 2e - 3 a(2)= 2e - 31! + e - 12! + 13! + ... = 72 e - 6
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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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e = 2.7182818 ......是欧拉常数。
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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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可以证明a(n)是形式
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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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```
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A(n) e + B(n)n! for integers A(n) and B(n).
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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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例如a(10)=
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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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```
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328161643 e − 65269448610! .
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```
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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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求A(109)+ B(109)并给出答案mod 77 777 777。
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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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`euler330()`应该返回15955822。
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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(euler330(), 15955822);
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2018-10-10 22:03:03 +00:00
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```
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2020-08-13 15:24:35 +00:00
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2020-12-16 07:37:30 +00:00
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# --solutions--
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