%I
%S 0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,2,0,0,1,2,0,2,0,0,1,1,0,3,
%T 0,0,0,2,0,2,0,0,1,2,0,3,0,0,1,3,0,3,0,0,1,2,0,4,0,0,1,2,0,4,0,0,0,2,
%U 0,4,0,0,1,4,0,4,0,0,0,4,0,4,0,0,1,4,0,4,0,0,1,3,0,5,0,0,0,3,0,5,0,0,1,4,0
%N Number of representations of n as a sum of two primes that are congruent modulo 3.
%e 22 can be written in two ways as the sum of two congruent primes modulo 3: 22 = 5 + 17 (5 = 17 mod 3) and 22 = 11 + 11 (order of addition is ignored). Hence a(22) = 2.
%t f[n_] := Module[{a, d, i}, a = {}; u = Floor[n/2]; For[i = 1, i <= u, i++, If[PrimeQ[i] && PrimeQ[n  i] && Mod[i, 3] != Mod[n  i, 3], a = Append[a, {n, i, n  i}]]]; a]; Table[Length[f[n]], {n, 1, 200}]
%Y Cf. A074169, A078647, A078648.
%K nonn
%O 1,22
%A _Joseph L. Pe_, Dec 13 2002
