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curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-330-eulers-number.md

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+---
+id: 5900f4b71000cf542c50ffc9
+title: 'Problem 330: Euler''s Number'
+challengeType: 5
+forumTopicId: 301988
+dashedName: problem-330-eulers-number
+---
+
+# --description--
+
+An infinite sequence of real numbers a(n) is defined for all integers n as follows:
+
+<!-- TODO Use MathJax and re-write from projecteuler.net -->
+
+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.
+
+# --hints--
+
+`euler330()` should return 15955822.
+
+```js
+assert.strictEqual(euler330(), 15955822);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function euler330() {
+
+  return true;
+}
+
+euler330();
+```
+
+# --solutions--
+
+```js
+// solution required
+```