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%I #10 Jan 14 2018 17:03:04
%S 0,0,0,0,0,0,1,2,0,2,2,0,2,2,0,2,3,2,1,3,3,3,3,5,4,2,5,3,3,1,2,5,6,1,
%T 5,6,4,5,6,4,4,5,4,4,8,4,4,7,3,5,8,5,4,8,6,6,10,6,5,10,3,5,10,2,7,9,5,
%U 5,7,7,7,10,5,5,12,3,8,11,4,8,8,5,5,13,9,5,11,7
%N Number of Goldbach partitions (p,q) of 2n such that there exists a prime r in p < r < q that does not appear as a part in any Goldbach partition of p+q = 2n.
%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) = A002375(n) - A278700(n).
%F a(n) = Sum_{i=3..n} (A010051(i) * A010051(2n-i) * (1 - Product_{k=i..n} (1 - abs(A010051(k) - A010051(2n-k))))).
%Y Cf. A002375, A010051, A278700.
%K nonn,easy
%O 1,8
%A _Wesley Ivan Hurt_, Dec 06 2016
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