A074169 Number of representations of n as a sum of two primes that are not congruent modulo 3.

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

Links

Table of n, a(n) for n=1..105.

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

Cf. A078646, A078647, A078648.

Sequence in context: A243223 A034178 A317531 * A363859 A328458 A099362

Adjacent sequences: A074166 A074167 A074168 * A074170 A074171 A074172

Keyword

nonn

Author

Joseph L. Pe, Dec 13 2002

Status

approved