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 A062303 #18 Mar 25 2023 17:04:28
%S A062303 1,0,1,1,1,2,2,3,3,5,6,7,8,9,9,11,13,14,15,16,17,18,19,21,24,25,26,26,
%T A062303 27,27,33,34,36,37,40,41,42,44,45,47,49,50,53,54,54,55,59,64,65,66,66,
%U A062303 68,69,72,74,76,78,79,80,81,82,85,91,92,93,93,99,101,105,106,106,108
%N A062303 Number of ways writing the n-th prime as a sum of two nonprimes.
%F A062303 A062610(A000040(n)) = number of [nonprime+composite] partitions of p(n).
%e A062303 n=10,p(10)=29 has 14 partitions of form a+b=29; 1+28=4+25=8+21=9+20=14+15 are the 5 relevant partitions, so a(10)=5.
%t A062303 Table[c = 0; Do[If[i + j == Prime[n] && ! PrimeQ[i] && ! PrimeQ[j], c = c + 1], {i, Prime[n] - 1}, {j, i}]; c, {n, 72}] (* _Jayanta Basu_, Apr 22 2013 *)
%t A062303 cnpQ[{a_,b_}]:=(!PrimeQ[a]&&CompositeQ[b])||(!PrimeQ[b]&&CompositeQ[a]); Join[{1},Table[Length[Select[IntegerPartitions[Prime[n],{2}],cnpQ]],{n,2,80}]] (* _Harvey P. Dale_, Sep 30 2018 *)
%Y A062303 Cf. A061358, A062602, A062610, A000040, A014092, A025584.
%K A062303 nonn
%O A062303 1,6
%A A062303 _Labos Elemer_, Jul 05 2001
%E A062303 Offset and name corrected by _Sean A. Irvine_, Mar 25 2023