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 A350883 #7 Jan 27 2022 21:06:58
%S A350883 0,0,0,0,2,2,3,2,3,2,8,0,5,2,10,2,8,0,12,2,10,2,19,0,23,2,23,0,16,0,
%T A350883 31,2,16,2,36,0,42,0,26,2,31,0,48,2,23,2,48,0,59,2,42,0,39,0,71,2,35,
%U A350883 0,62,0,108,2,53,2,59,0,96,0,38,2,83,0,108,2,91,2,77,0,127
%N A350883 Sum of the smaller parts of the partitions of n into two prime parts.
%H A350883 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A350883 a(n) = Sum_{k=1..floor(n/2)} c(k) * c(n-k) * k, where c = A010051.
%F A350883 a(n) = Sum_{k=floor((n-1)^2/4)+1..floor(n^2/4)} c(2k-1) * c(2k) * A339399(2k-1), where c = A350866.
%e A350883 a(10) = 8; The partitions of 10 into two prime parts are (7,3) and (5,5). The sum of the smaller parts of these partitions is then 5+3 = 8.
%o A350883 (PARI) a(n) = sum(k=1, n\2, if (isprime(k) && isprime(n-k), k)); \\ _Michel Marcus_, Jan 21 2022
%Y A350883 Cf. A010051, A339399, A350865 (larger parts), A350866.
%K A350883 nonn
%O A350883 0,5
%A A350883 _Wesley Ivan Hurt_, Jan 20 2022