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 A382871 #34 Apr 10 2025 08:34:33
%S A382871 1,0,0,0,0,1,0,1,0,0,0,0,0,1,1,1,1,1,2,3,3,2,3,4,6,2,5,0,5,9,7,14,8,6,
%T A382871 10,9,21,19,11,18,15,29,34,35,34,24,31,51,55,48,76,34,60,93,89,97,91,
%U A382871 76,83,156,164,189,145,157,172,186,283,276,218,242,280,405,433,476,446
%N A382871 Number of ways to partition distinct prime numbers into two disjoint sets such that the sum of each set equals n.
%C A382871 Conjecture: a(n) > 0 for n > 27.
%F A382871 a(n) = 1/2 * [(x*y)^n] Product_{p prime} (1 + x^p + y^p) for n > 0.
%e A382871 a(18) = 2: [13, 5; 11, 7], [13, 3, 2; 11, 7].
%e A382871 a(19) = 3: [19; 17, 2], [19; 11, 5, 3], [17, 2; 11, 5, 3].
%o A382871 (PARI) a(n) = my(x='x+O('x^(n+1)), y='y+O('y^(n+1)));if(n==0, 1, polcoef(polcoef(prod(k=1, n, 1+x^prime(k)+y^prime(k)), n), n)/2);
%Y A382871 Cf. A000607, A108796, A382954.
%K A382871 nonn
%O A382871 0,19
%A A382871 _Seiichi Manyama_, Apr 09 2025