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A152788
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Integers, n, such that (n^3)/3 is the average of a pair of twin primes.
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1
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6, 30, 84, 144, 186, 204, 270, 360, 516, 576, 726, 756, 810, 990, 1020, 1140, 1446, 1500, 1836, 2010, 2250, 2304, 2820, 3204, 3366, 3564, 4170, 4320, 4344, 4416, 4590, 4656, 5160, 5220, 5820, 5976, 6120, 6204, 6276, 6534, 6876, 7260, 7710, 7806, 7866, 8256
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| (6^3)/3=72~71,72,73; (30^3)/3=9000~8999,9000,9001;...
These are the integers of the form (3*A014574(i))^(1/3), any index i. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 14 2008]
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MATHEMATICA
| lst1={}; lst2={}; Do[ p1=Prime[n]; p2=Prime[n+1]; If[p2-p1==2, e=(3*(p1+1))^(1/3); i=Floor[e]; If[e==i, AppendTo[lst1, (p1+1)]; AppendTo[lst2, i]]], {n, 2*10!}]; Print[lst1]; Print[lst2]
fQ[n_] := PrimeQ[n^3/3 - 1] && PrimeQ[n^3/3 + 1]; lst = {}; Do[If[fQ@n, AppendTo[lst, n]], {n, 3, 10^4, 3}]; lst
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CROSSREFS
| Cf. A152786,A152787
Sequence in context: A038039 A050972 A002444 * A055112 A094143 A009775
Adjacent sequences: A152785 A152786 A152787 * A152789 A152790 A152791
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KEYWORD
| nonn
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 12 2008
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 14 2008
Corrected divisor in definition. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 20 2008
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