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.
%I A110589 #16 Sep 08 2022 08:45:20
%S A110589 3,5,7,11,13,19,23,29,31,37,41,47,67,73,79,97,101,103,109,151,157,197,
%T A110589 211,227,233,239,257,263,293,307,331,337,349,353,359,367,389,397,409,
%U A110589 443,449,463,487,491,509,521,547,569,571,587,613,619,653,661,673,727
%N A110589 Primes p such that 2*q+3 = p^2, where q is prime.
%H A110589 Amiram Eldar, <a href="/A110589/b110589.txt">Table of n, a(n) for n = 1..10000</a>
%p A110589 ispower := proc(n,b) andmap(proc(w) evalb(w[2] mod b = 0) end, ifactors(n)[2]) end: a:=2: SQRTP||a:=[]; for z from 1 to 1 do for n from 1 to 10000 do p:=ithprime(n); m:=a*p+a+1; if ispower(m,2) and isprime(sqrt(m)) then SQRTP||a:=[op(SQRTP||a),sqrt(m)] fi od; od; SQRTP||a;
%t A110589 fQ[n_] := PrimeQ[(n^2 - 3)/2]; Select[ Prime@ Range@129, fQ@# &] (* _Robert G. Wilson v_, Jun 19 2006 *)
%t A110589 Select[Table[Sqrt[2 Prime[n] + 3], {n, 1, 30000}], PrimeQ] (* _Vincenzo Librandi_, Mar 19 2015 *)
%o A110589 (Magma) [p: p in PrimesUpTo(1000) | IsPrime((p^2-3) div 2)]; // _Vincenzo Librandi_, Mar 19 2015
%Y A110589 Cf. A098828, A109358.
%K A110589 nonn
%O A110589 1,1
%A A110589 _Walter Kehowski_, Sep 13 2005
%E A110589 More terms from _Robert G. Wilson v_, Jun 19 2006