This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A295630 #15 May 18 2021 11:44:06
%S A295630 0,0,1,1,1,2,2,2,3,3,5,4,5,5,6,5,8,6,8,7,9,8,11,8,11,10,13,11,14,11,
%T A295630 14,13,15,13,17,13,18,17,18,16,20,16,20,18,21,19,23,18,23,20,25,22,26,
%U A295630 21,26,24,28,25,29,23,29,28,30,26,32,26,33,31,33,29
%N A295630 Number of partitions of n into two distinct parts that are not both prime.
%H A295630 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%H A295630 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A295630 a(n) = Sum_{i=1..floor((n-1)/2)} 1 - A010051(i)*A010051(n-i).
%e A295630 a(12) = 4; The partitions of 12 into two distinct parts are (11,1), (10,2), (9,3), (8,4) and (7,5). Of these partitions, the parts in (11,1), (10,2), (9,3) and (8,4) are not both prime, so a(12) = 4.
%t A295630 Table[Sum[1 - (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[(n - 1)/2]}], {n, 80}]
%t A295630 Table[Count[IntegerPartitions[n,{2}],_?(#[[1]]!=#[[2]]&&Total[Boole[ PrimeQ[ #]]]<2&)],{n,70}] (* _Harvey P. Dale_, May 18 2021 *)
%Y A295630 Cf. A010051, A295629.
%K A295630 nonn,easy
%O A295630 1,6
%A A295630 _Wesley Ivan Hurt_, Nov 24 2017