Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Dec 17 2019 07:40:15
%S 18,72,882,1152,2592,3528,4050,15138,20808,34848,46818,69192,83232,
%T 103968,112338,149058,176418,180000,206082,281250,362952,388962,
%U 438048,472392,478242,538722,649800,734472,808992,960498,1080450,1143072
%N Averages of twin prime pairs k such that k*2 and k/2 are squares.
%H Amiram Eldar, <a href="/A154670/b154670.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 18*A037073(n)^2. - _M. F. Hasler_, Jan 15 2009
%e 18/2 = 9 = 3^2, 18*2 = 36 = 6^2.
%t lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=Sqrt[n*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=Sqrt[n/2];If[Floor[s]==s,AppendTo[lst,n]]],{n,6,10!,6}];lst
%o (PARI) for(i=1,999, isprime(18*i^2+1) && isprime(18*i^2-1) && print1(18*i^2",")) \\ _M. F. Hasler_, Jan 15 2009
%Y Cf. A037073.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 13 2009