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

Author

Vladimir Joseph Stephan Orlovsky, Dec 12 2008

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A014574, A152786, A152787.

Programs

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

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

Extensions

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

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