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%I #17 Mar 05 2021 16:50:28
%S 1,1,1,2,4,3,4,6,6,6,8,9,9,9,11,9,13,15,10,14,16,14,16,19,18,17,21,18,
%T 20,25,18,24,27,19,26,28,25,27,32,26,28,35,29,29,39,30,32,38,30,37,41,
%U 35,37,42,38,41,47,40,40,54,38,42,53,39,48,52,46,46
%N Number of partitions of 2n into two prime parts or two nonprime parts.
%H Alois P. Heinz, <a href="/A291563/b291563.txt">Table of n, a(n) for n = 1..20000</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..n} [A010051(i) = A010051(2n-i)], where [] is the Iverson bracket.
%F a(n) = n - A291564(n).
%p a:= n-> n-add(`if`(isprime(n+i) xor isprime(n-i), 1, 0), i=1..n-1):
%p seq(a(n), n=1..80); # _Alois P. Heinz_, Mar 05 2021
%t Table[Sum[KroneckerDelta[(PrimePi[k] - PrimePi[k - 1]), (PrimePi[2 n - k] - PrimePi[2 n - 1 - k])], {k, n}], {n, 80}]
%Y Cf. A010051, A291564.
%K nonn,easy
%O 1,4
%A _Wesley Ivan Hurt_, Oct 20 2017