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A154671 Averages of twin prime pairs n such that n*3 and n/3 are squares. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..31.

FORMULA

a(n) = 12*A154331(n)^2 [From 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", ")) [From M. F. Hasler, Jan 15 2009]

CROSSREFS

Cf. A154670

Sequence in context: A166755 A230712 A271559 * A241230 A037972 A111990

Adjacent sequences:  A154668 A154669 A154670 * A154672 A154673 A154674

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

STATUS

approved

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Last modified May 26 01:26 EDT 2017. Contains 287073 sequences.