A226068 The sum of the positive integers not exceeding 2n that are representable as the sum of two successive sexy primes.

0, 0, 0, 0, 0, 0, 0, 16, 16, 36, 36, 36, 36, 64, 64, 96, 96, 96, 96, 136, 136, 136, 136, 136, 136, 188, 188, 188, 188, 188, 188, 188, 188, 256, 256, 256, 256, 256, 256, 336, 336, 336, 336, 424, 424, 424, 424, 424

Offset: 1

Author

Wesley Ivan Hurt, May 24 2013

Keywords

• nonn

Comments

4 divides a(n) for n > 0.

Crossrefs

Cf. A000720, A104010, A098428.

Programs

Maple

with(numtheory); A226068:=n->sum( 2*i*(pi(i-3) - pi(i-4)) * (pi(i+3) - pi(i+2)) , i = 1..n);
seq(A226068(k), k = 1..70);

Formula

a(n) = 2*Sum_{i=1..n} i * (pi(i-3) - pi(i-4)) * (pi(i+3) - pi(i+2)), where pi is the prime counting function (A000720).

a(n) = Sum_{i=1..2*n} c(i), where c is the characteristic function of A104010. - R. J. Mathar, May 28 2013