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id	title	challengeType	forumTopicId	dashedName
5900f5141000cf542c510027	Problem 423: Consecutive die throws	5	302093	problem-423-consecutive-die-throws

--description--

Let n be a positive integer.

A 6-sided die is thrown n times. Let c be the number of pairs of consecutive throws that give the same value.

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.

--hints--

euler423() should return 653972374.

assert.strictEqual(euler423(), 653972374);

--seed--

--seed-contents--

function euler423() {

  return true;
}

euler423();

--solutions--

// solution required

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