1.5 KiB
1.5 KiB
id | challengeType | title |
---|---|---|
5900f5141000cf542c510027 | 5 | Problem 423: Consecutive die throws |
Description
For example, if n = 7 and the values of the die throws are (1,1,5,6,6,6,3), then the following pairs of consecutive throws give the same value: (1,1,5,6,6,6,3) (1,1,5,6,6,6,3) (1,1,5,6,6,6,3) Therefore, c = 3 for (1,1,5,6,6,6,3).
Define C(n) as the number of outcomes of throwing a 6-sided die n times such that c does not exceed π(n).1 For example, C(3) = 216, C(4) = 1290, C(11) = 361912500 and C(24) = 4727547363281250000.
Define S(L) as ∑ C(n) for 1 ≤ n ≤ L. For example, S(50) mod 1 000 000 007 = 832833871.
Find S(50 000 000) mod 1 000 000 007.
1 π denotes the prime-counting function, i.e. π(n) is the number of primes ≤ n.
Instructions
Tests
tests:
- text: <code>euler423()</code> should return 653972374.
testString: assert.strictEqual(euler423(), 653972374, '<code>euler423()</code> should return 653972374.');
Challenge Seed
function euler423() {
// Good luck!
return true;
}
euler423();
Solution
// solution required