%I #16 Sep 08 2022 08:45:46
%S 5,11,19,41,89,109,239,271,379,461,599,929,991,2069,2969,3079,4159,
%T 4421,4969,5851,9311,10099,13109,13339,14519,16001,20021,23869,25439,
%U 28729,30449,32579,34039,38219,39799,48619,50849,53591,57839,59779,60761
%N Primes of the form ((p+1)/2)^2+((p-1)/2), where p is prime.
%C Subsequence of A002327. - _Charles R Greathouse IV_, Aug 11 2009
%H Vincenzo Librandi, <a href="/A163419/b163419.txt">Table of n, a(n) for n = 1..3000</a>
%e ((3+1)/2)^2+((3-1)/2) = 4+1 = 5;
%e ((5+1)/2)^2+((5-1)/2) = 9+2 = 11;
%e ((7+1)/2)^2+((7-1)/2) = 16+3 = 19.
%t f[n_]:=((p+1)/2)^2+((p-1)/2); lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst,f[p]]],{n,6!}];lst
%t Select[((#+1)/2)^2+(#-1)/2&/@Prime[Range[500]],PrimeQ] (* _Harvey P. Dale_, Nov 25 2012 *)
%o (Magma) [a: p in PrimesInInterval(3, 600) | IsPrime(a) where a is (p^2 + 4*p - 1) div 4]; // _Vincenzo Librandi_, Sep 17 2016
%o (PARI) lista(nn) = forprime(p=3, nn, if(isprime(P=(p^2+4*p-1)/4), print1(P, ", "))); \\ _Altug Alkan_, Sep 17 2016
%Y Cf. A002327, A162652, A163418.
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 27 2009