1.2 KiB
1.2 KiB
id | challengeType | title | forumTopicId |
---|---|---|---|
5900f4b71000cf542c50ffc9 | 5 | Problem 330: Euler's Number | 301988 |
Description
An infinite sequence of real numbers a(n) is defined for all integers n as follows:
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
with e = 2.7182818... being Euler's constant.
It can be shown that a(n) is of the form
A(n) e + B(n)n! for integers A(n) and B(n).
For example a(10) =
328161643 e − 65269448610!.
Find A(109) + B(109) and give your answer mod 77 777 777.
Instructions
Tests
tests:
- text: <code>euler330()</code> should return 15955822.
testString: assert.strictEqual(euler330(), 15955822);
Challenge Seed
function euler330() {
// Good luck!
return true;
}
euler330();
Solution
// solution required