%I A074169
%S A074169 0,0,0,0,1,0,0,1,1,1,0,1,0,1,1,1,0,2,0,1,1,1,0,3,0,1,0,0,0,3,0,1,1,1,0,
%T A074169 4,0,0,1,1,0,4,0,1,1,1,0,5,0,1,0,0,0,5,0,1,0,0,0,6,0,1,1,1,0,6,0,0,1,1,
%U A074169 0,6,0,1,1,1,0,7,0,0,1,1,0,8,0,1,0,0,0,9,0,1,0,0,0,7,0,0,1,1,0,8,0,1,1
%N A074169 Number of representations of n as a sum of two primes that are not congruent 
               modulo 3.
%e A074169 18 can be written in two ways as the sum of two incongruent primes modulo 
               3: 18 = 5 + 13 (5 = 2 mod 3; 13 = 1 mod 3) and 18 = 7 + 11 (order 
               of addition is ignored). Hence a(18) = 2.
%t A074169 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 A074169 Cf. A078646, A078647, A078648.
%Y A074169 Sequence in context: A088434 A034178 A131341 this_sequence A099362 A058940 
               A141684
%Y A074169 Adjacent sequences: A074166 A074167 A074168 this_sequence A074170 A074171 
               A074172
%K A074169 nonn
%O A074169 1,18
%A A074169 Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 13 2002