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Search: id:A078647
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| A078647 |
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Smallest integer that can be written in exactly n ways as the sum of two primes that are congruent modulo 3. |
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+0
3
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| 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; listen)
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OFFSET
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1,1
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EXAMPLE
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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.
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MATHEMATICA
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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
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CROSSREFS
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Cf. A074169, A078646, A078648.
Sequence in context: A036920 A036921 A083510 this_sequence A031108 A163484 A020173
Adjacent sequences: A078644 A078645 A078646 this_sequence A078648 A078649 A078650
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 13 2002
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 19 2002
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