55 lines
966 B
Markdown
55 lines
966 B
Markdown
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---
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id: 5900f4b71000cf542c50ffc9
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title: 'Problem 330: Euler''s Number'
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challengeType: 5
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forumTopicId: 301988
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dashedName: problem-330-eulers-number
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---
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# --description--
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An infinite sequence of real numbers a(n) is defined for all integers n as follows:
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<!-- TODO Use MathJax and re-write from projecteuler.net -->
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For example,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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with e = 2.7182818... being Euler's constant.
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It can be shown that a(n) is of the form
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A(n) e + B(n)n! for integers A(n) and B(n).
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For example a(10) =
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328161643 e − 65269448610!.
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Find A(109) + B(109) and give your answer mod 77 777 777.
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# --hints--
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`euler330()` should return 15955822.
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```js
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assert.strictEqual(euler330(), 15955822);
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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 euler330() {
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return true;
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}
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euler330();
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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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