A154671 Averages of twin prime pairs k such that k*3 and k/3 are squares.

12, 108, 192, 432, 1452, 2028, 3468, 4800, 10092, 18252, 106032, 139968, 221952, 284592, 299568, 355008, 549552, 618348, 720300, 786432, 823728, 961068, 995328, 1009200, 1138368, 1190700, 1291008, 1529388, 1537968, 1651692, 1948908

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Keywords

• nonn

Examples

			12*3 = 36 = 6^2, 12/3 = 4 = 2^2.
		

Links

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

Crossrefs

Cf. A154670.

Programs

Mathematica

lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n*3)^(1/2); If[Floor[s]==s,AppendTo[lst,n]]],{n,6,10!,6}]; lst...and/or... lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n/3)^(1/2); If[Floor[s]==s,AppendTo[lst,n]]],{n,6,10!,6}]; lst
Select[Mean/@Select[Partition[Prime[Range[150000]],2,1],#[[2]]-#[[1]] == 2&],AllTrue[{Sqrt[#/3],Sqrt[3#]},IntegerQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 06 2015 *)

PARI

for(i=1,999, isprime(12*i^2+1) && isprime(12*i^2-1) && print1(12*i^2",")) \\ M. F. Hasler, Jan 15 2009

Formula

a(n) = 12*A154331(n)^2. - M. F. Hasler, Jan 15 2009