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A078647 Smallest integer that can be written in exactly n ways as the sum of two primes that are congruent modulo 3. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 29 14:46 EDT 2022. Contains 354913 sequences. (Running on oeis4.)