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%I #3 Feb 11 2014 19:05:33
%S 4,22,34,58,94,112,142,170,220,274,286,340,280,364,460,622,520,490,
%T 610,650,670,890,920,700,850,770,1000,1250,1160,910,1520,1190,1120,
%U 1400,1450,1670,1570,1660,1630,1330,1610,1870,2002,2260,2060,1540,1750,1960
%N Smallest integer that can be written in exactly n ways as the sum of two primes that are congruent modulo 3.
%e 22 is the first integer that can be written in exactly 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(2) = 22.
%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, {50}]; Do[l = Length[ f[n]]; If[l < 51 && a[[l]] == 0, a[[l]] = n], {n, 1, 2000}]; a
%Y Cf. A074169, A078646, A078648.
%K nonn
%O 1,1
%A _Joseph L. Pe_, Dec 13 2002
%E Edited and extended by _Robert G. Wilson v_, Dec 19 2002
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