|
%I #15 Dec 17 2019 07:40:53
%S 12,108,192,432,1452,2028,3468,4800,10092,18252,106032,139968,221952,
%T 284592,299568,355008,549552,618348,720300,786432,823728,961068,
%U 995328,1009200,1138368,1190700,1291008,1529388,1537968,1651692,1948908
%N Averages of twin prime pairs k such that k*3 and k/3 are squares.
%H Amiram Eldar, <a href="/A154671/b154671.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 12*A154331(n)^2. - _M. F. Hasler_, Jan 15 2009
%e 12*3 = 36 = 6^2, 12/3 = 4 = 2^2.
%t 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
%t 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 *)
%o (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
%Y Cf. A154670.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 13 2009
|
