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freeCodeCamp/curriculum/challenges/japanese/10-coding-interview-prep/project-euler/problem-330-eulers-number.md
2022-01-20 20:30:18 +01:00

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id, title, challengeType, forumTopicId, dashedName
id title challengeType forumTopicId dashedName
5900f4b71000cf542c50ffc9 Problem 330: Euler's Number 5 301988 problem-330-eulers-number

--description--

An infinite sequence of real numbers a(n) is defined for all integers n as follows:

a(n) = \begin{cases} 1 & n < 0 \\\\ \displaystyle \sum_{i = 1}^{\infty} \frac{a(n - 1)}{i!} & n \ge 0 \end{cases}

For example,

\begin{align} & a(0) = \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = e 1 \\\\ & a(1) = \frac{e 1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = 2e 3 \\\\ & a(2) = \frac{2e 3}{1!} + \frac{e 1}{2!} + \frac{1}{3!} + \ldots = \frac{7}{2} e 6 \end{align}

with e = 2.7182818\ldots being Euler's constant.

It can be shown that a(n) is of the form \displaystyle\frac{A(n)e + B(n)}{n!} for integers A(n) and B(n).

For example \displaystyle a(10) = \frac{328161643e 652694486}{10!}.

Find A({10}^9) + B({10}^9) and give your answer \bmod 77\\,777\\,777.

--hints--

eulersNumber() should return 15955822.

assert.strictEqual(eulersNumber(), 15955822);

--seed--

--seed-contents--

function eulersNumber() {

  return true;
}

eulersNumber();

--solutions--

// solution required