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A074169
Number of representations of n as a sum of two primes that are not congruent modulo 3.
2
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, 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, 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
OFFSET
1,18
EXAMPLE
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.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Dec 13 2002
STATUS
approved