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 A078646 Number of representations of n as a sum of two primes that are congruent modulo 3. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,22 LINKS 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}] CROSSREFS Cf. A074169, A078647, A078648. Sequence in context: A325192 A087773 A025867 * A264405 A304650 A347992 Adjacent sequences:  A078643 A078644 A078645 * A078647 A078648 A078649 KEYWORD nonn AUTHOR Joseph L. Pe, Dec 13 2002 STATUS approved

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Last modified August 14 10:58 EDT 2022. Contains 356116 sequences. (Running on oeis4.)