1.4 KiB
1.4 KiB
id | challengeType | title | forumTopicId |
---|---|---|---|
5900f50d1000cf542c51001f | 5 | Problem 417: Reciprocal cycles II | 302086 |
Description
1/2= 0.5 1/3= 0.(3) 1/4= 0.25 1/5= 0.2 1/6= 0.1(6) 1/7= 0.(142857) 1/8= 0.125 1/9= 0.(1) 1/10= 0.1
Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
Unit fractions whose denominator has no other prime factors than 2 and/or 5 are not considered to have a recurring cycle. We define the length of the recurring cycle of those unit fractions as 0.
Let L(n) denote the length of the recurring cycle of 1/n. You are given that ∑L(n) for 3 ≤ n ≤ 1 000 000 equals 55535191115.
Find ∑L(n) for 3 ≤ n ≤ 100 000 000
Instructions
Tests
tests:
- text: <code>euler417()</code> should return 446572970925740.
testString: assert.strictEqual(euler417(), 446572970925740);
Challenge Seed
function euler417() {
// Good luck!
return true;
}
euler417();
Solution
// solution required