A279481 - OEIS

%I #22 Jan 30 2021 23:57:06

%S 0,0,1,2,4,2,5,8,6,9,13,12,14,10,12,12,24,22,9,20,24,27,29,38,36,24,

%T 39,29,33,43,24,58,58,17,52,60,53,63,80,46,54,87,70,46,100,62,58,87,

%U 31,79,104,71,87,119,99,116,152,114,94,181,54,82,144,39,116,133

%N Count the primes appearing in each interval [p,q] where (p,q) is a Goldbach partition of 2n, and then add the results.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{i=2..n} A010051(i)*A010051(2*n-i)*(pi(2*n-i)-pi(i-1)) for n > 2.

%p with(numtheory): A279481:=n->add( (pi(i)-pi(i-1)) * (pi(2*n-i)-pi(2*n-i-1)) * (pi(2*n-i)-pi(i-1)), i=2..n): 0,0,seq(A279481(n), n=3..100);

%t f[n_] := Sum[ Boole[ PrimeQ[ i]] Boole[ PrimeQ[ 2n -i]] (PrimePi[ 2n -i] - PrimePi[i -1]), {i, 2, n}]; f[2] = 0; Array[ f, 80] (* _Robert G. Wilson v_, Dec 15 2016 *)

%Y Cf. A000720, A010051, A045917, A278700, A279103.

%K nonn,easy

%O 1,4

%A _Wesley Ivan Hurt_, Dec 12 2016