A078648 Smallest integer that can be written in exactly n ways as the sum of two primes that are not congruent modulo 3.

5, 18, 24, 36, 48, 60, 78, 84, 90, 114, 144, 120, 168, 180, 234, 246, 288, 240, 210, 324, 300, 360, 474, 330, 528, 576, 390, 462, 480, 420, 570, 510, 672, 792, 756, 876, 714, 798, 690, 1038, 630, 1008, 930, 780, 960, 870, 924, 900, 1134, 1434, 840, 990, 1302

Offset

1,1

Links

Table of n, a(n) for n=1..53.

Example

18 is the first integer that can be written in exactly two ways as the sum of two congruent primes modulo 3: 18 = 5 + 13 = 7 + 11 (order of addition is ignored). Hence a(2) = 18.

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]; a = Table[0, {55}]; Do[l = Length[ f[n]]; If[l < 56 && a[[l]] == 0, a[[l]] = n], {n, 1, 2500}]; a

Crossrefs

Sequence in context: A178365 A345912 A022142 * A364607 A035338 A055371

Adjacent sequences: A078645 A078646 A078647 * A078649 A078650 A078651

Keyword

nonn

Author

Joseph L. Pe, Dec 13 2002

Extensions

Edited and extended by Robert G. Wilson v, Dec 19 2002

Status

approved