This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
for (i=1,1500,if(isprime(i) && isprime(2*prime(i)^2-1),print1(i,",")))
for (i=1,1500,if(isprime(i) && !isprime(2*prime(i)^2-1),print1(i,",")))
[p: p in PrimesUpTo(2500)| IsPrime(2*p^2-1)]; // Vincenzo Librandi, Jan 29 2011
q:= p-> andmap(isprime, [p, 2*p^2-1]): select(q, [$2..2000])[]; # Alois P. Heinz, Jun 21 2022
Select[Table[Prime[n], {n, 500}], PrimeQ[2*#^2 - 1] &] (* Ray Chandler, May 03 2005 *)
lst={};Do[p=Prime[n];If[PrimeQ[r=2*p^2-1],AppendTo[lst,r]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 20 2009 *)
Select[2#^2-1&/@Prime[Range[200]],PrimeQ] (* Harvey P. Dale, Jun 26 2017 *)
for (i=1,300,if(isprime(2*prime(i)^2-1),print1(2*prime(i)^2-1,",")))
[n: n in [1..220]| not IsPrime(2*NthPrime(n)^2-1)];
Select[Range[200], !PrimeQ[2Prime[#]^2 - 1]&]