A152788 Integers k such that (k^3)/3 is the average of a pair of twin primes.

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

Offset

1,1

Comments

These are the integers of the form (3*A014574(i))^(1/3), any index i. - R. J. Mathar, Dec 14 2008

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

6 is a term since (6^3)/3 = 72 and (71, 73) are twin primes.
30 is a term since (30^3)/3 = 9000 and (8999, 9001) are twin primes.

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

Prog

(Magma) [k:k in [3..9000 by 3]| IsPrime(k^3 div 3 -1) and IsPrime(k^3 div 3 +1)]; // Marius A. Burtea, Jan 01 2020

Crossrefs

Cf. A014574, A152786, A152787.

Sequence in context: A050972 A259918 A002444 * A055112 A094143 A217260

Adjacent sequences: A152785 A152786 A152787 * A152789 A152790 A152791

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 12 2008

Extensions

Edited and extended by Robert G. Wilson v, Dec 14 2008

Corrected divisor in definition. - R. J. Mathar, Dec 20 2008

Status

approved