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A279794 Number of Goldbach partitions (p,q) of 2n such that |p-q| > n.

%I A279794 #19 Feb 16 2025 08:33:38
%S A279794 0,0,0,0,0,0,1,1,0,1,2,1,1,1,1,1,2,2,1,1,1,2,2,3,2,2,3,2,2,2,1,3,3,1,
%T A279794 3,3,3,3,5,3,2,4,4,2,4,3,3,4,1,3,4,2,4,4,3,4,5,4,4,6,2,3,5,2,4,5,3,3,
%U A279794 4,3,4,5,2,2,5,2,4,5,3,4,5,3,3,8,5,3,6,4,4,8,4,4,7,3,4,6,5,6,7,5
%N A279794 Number of Goldbach partitions (p,q) of 2n such that |p-q| > n.
%H A279794 Robert Israel, <a href="/A279794/b279794.txt">Table of n, a(n) for n = 1..10000</a>
%H A279794 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>
%H A279794 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%H A279794 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A279794 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A279794 a(n) = Sum_{i=3..n-1} A010051(i) * A010051(2n-i) * (1-sign(floor(n/(2*(n-i))))).
%p A279794 with(numtheory): A279794:=n->add( (pi(i)-pi(i-1)) * (pi(2*n-i)-pi(2*n-i-1)) * (1-signum(floor(n/(2*(n-i))))), i=3..n-1): seq(A279794(n), n=1..100);
%p A279794 # Alternative:
%p A279794 f:= proc(n) local p;
%p A279794    nops(select(t -> isprime(t) and isprime(2*n-t), [seq(p,p=3..(n-1)/2,2)]))
%p A279794 end proc:
%p A279794 map(f, [$1..100]); # _Robert Israel_, Feb 15 2021
%t A279794 Table[Sum[Boole[PrimeQ@ i] Boole[PrimeQ[2 n - i]] (1 - Sign@ Floor[n/(2 (n - i))]), {i, 3, n - 1}], {n, 100}] (* _Michael De Vlieger_, Dec 21 2016 *)
%Y A279794 Cf. A010051, A002375, A279792.
%K A279794 nonn,easy
%O A279794 1,11
%A A279794 _Wesley Ivan Hurt_, Dec 18 2016