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 A224715 #12 Aug 11 2015 05:12:43
%S A224715 0,0,0,1,4,3,6,5,8,9,8,11,12,11,14,15,16,15,18,19,18,21,22,23,24,25,
%T A224715 24,27,26,29,30,31,32,31,34,33,36,37,38,39,40,39,42,41,44,43,46,47,48,
%U A224715 47,50,51,50,53,54,55,56,55,58,59,58,61,62,63,62,65,66
%N A224715 The number of unordered partitions {a,b} of prime(n) such that a or b is a nonnegative composite and the other is prime.
%H A224715 J. Stauduhar, <a href="/A224715/b224715.txt">Table of n, a(n) for n = 1..5000</a>
%e A224715 For n = 5, prime(5) = 11. The pairwise partitions of 11 are {{10, 1}, {9, 2}, {8, 3}, {7, 4}, {6, 5}} and four partitions meet the requirements: {9, 2}, {8, 3}, {7, 4}, {6, 5}, so a(5) = 4.
%t A224715 nn = 100; mx = Prime[nn]; ps = Prime[Range[nn]]; notPs = Complement[Range[2, mx], ps]; t2 = Table[0, {Range[mx]}]; Do[s = i + j; If[s <= mx, t2[[s]]++], {i, ps}, {j, notPs}]; t2[[ps]] (* _T. D. Noe_, Apr 23 2013 *)
%Y A224715 Subsequence of A224712.
%Y A224715 Essentially the same as A062302.
%K A224715 nonn
%O A224715 1,5
%A A224715 _J. Stauduhar_, Apr 22 2013