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

1,1

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A154670.

Sequence in context: A166755 A230712 A271559 * A321672 A241230 A353047

Adjacent sequences: A154668 A154669 A154670 * A154672 A154673 A154674

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Status

approved