A078646 Number of representations of n as a sum of two primes that are congruent modulo 3.

0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 1, 1, 0, 3, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0, 3, 0, 0, 1, 3, 0, 3, 0, 0, 1, 2, 0, 4, 0, 0, 1, 2, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 1, 4, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 1, 4, 0, 4, 0, 0, 1, 3, 0, 5, 0, 0, 0, 3, 0, 5, 0, 0, 1, 4, 0

Offset

1,22

Links

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

Example

22 can be written in 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(22) = 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}]
Table[Count[Select[IntegerPartitions[n, {2}], AllTrue[#, PrimeQ]&], _?(Mod[#[[1]], 3]== Mod[ #[[2]], 3]&)], {n, 110}] (* Harvey P. Dale, Jul 14 2024 *)

Crossrefs

Cf. A074169, A078647, A078648.

Sequence in context: A325192 A087773 A025867 * A264405 A304650 A360670

Adjacent sequences: A078643 A078644 A078645 * A078647 A078648 A078649

Keyword

nonn

Author

Joseph L. Pe, Dec 13 2002

Status

approved