A078647 Smallest integer that can be written in exactly n ways as the sum of two primes that are congruent modulo 3.

4, 22, 34, 58, 94, 112, 142, 170, 220, 274, 286, 340, 280, 364, 460, 622, 520, 490, 610, 650, 670, 890, 920, 700, 850, 770, 1000, 1250, 1160, 910, 1520, 1190, 1120, 1400, 1450, 1670, 1570, 1660, 1630, 1330, 1610, 1870, 2002, 2260, 2060, 1540, 1750, 1960

Offset

1,1

Links

Table of n, a(n) for n=1..48.

Example

22 is the first integer that can be written in exactly 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(2) = 22.

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, {50}]; Do[l = Length[ f[n]]; If[l < 51 && a[[l]] == 0, a[[l]] = n], {n, 1, 2000}]; a

Crossrefs

Cf. A074169, A078646, A078648.

Sequence in context: A036921 A083510 A277586 * A031108 A350521 A163484

Adjacent sequences: A078644 A078645 A078646 * A078648 A078649 A078650

Keyword

nonn

Author

Joseph L. Pe, Dec 13 2002

Extensions

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

Status

approved