

A078648


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


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
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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 * A035338 A055371 A034098
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



