%I
%S 5,18,24,36,48,60,78,84,90,114,144,120,168,180,234,246,288,240,210,
%T 324,300,360,474,330,528,576,390,462,480,420,570,510,672,792,756,876,
%U 714,798,690,1038,630,1008,930,780,960,870,924,900,1134,1434,840,990,1302
%N Smallest integer that can be written in exactly n ways as the sum of two primes that are not congruent modulo 3.
%e 18 is the first integer that can be written in exactly two ways as the sum of two congruent primes modulo 3: 18 = 5 + 13 = 7 + 11 (order of addition is ignored). Hence a(2) = 18.
%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]; a = Table[0, {55}]; Do[l = Length[ f[n]]; If[l < 56 && a[[l]] == 0, a[[l]] = n], {n, 1, 2500}]; a
%K nonn
%O 1,1
%A _Joseph L. Pe_, Dec 13 2002
%E Edited and extended by _Robert G. Wilson v_, Dec 19 2002
