%I #22 Sep 08 2022 08:46:16
%S 13,29,73,101,353,409,601,673,829,1093,1289,1613,1973,2801,2953,3109,
%T 3433,4129,4889,5501,6373,6833,7069,7309,8053,9649,9929,10501,13933,
%U 16369,18229,19001,20593,21001,25301,26209,26669,28549,30493,31489,33013,33529,36709
%N Primes p such that 2*p + 23 is a square.
%C Primes of the form 2*k^2 + 2*k - 11.
%t Select[Prime[Range[5000]], IntegerQ[Sqrt[2 # + 23]] &]
%o (Magma) [p: p in PrimesUpTo(50000) | IsSquare(2*p + 23)];
%o (PARI) lista(nn) = forprime(p=2, nn, if (issquare(2*p+23), print1(p, ", "))); \\ _Michel Marcus_, Mar 22 2016
%o (Python)
%o from gmpy2 import is_prime,is_square
%o for p in range(3,10**6,2):
%o if(not is_square(2*p+23)):continue
%o elif(is_prime(p)):print(p)
%o # _Soumil Mandal_, Apr 07 2016
%Y Cf. A000040.
%Y Subsequence of A002144, A045433.
%Y Cf. similar sequences listed in A269784.
%K nonn
%O 1,1
%A _Vincenzo Librandi_, Mar 22 2016