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Primes p such that 2*p + 43 is a square.
1

%I #20 Sep 08 2022 08:46:16

%S 3,19,199,523,739,991,1279,2791,3259,6823,9091,12619,13591,15643,

%T 17839,32491,34039,37243,40591,63703,68059,72559,79579,86923,89443,

%U 105319,110899,137791,144163,153991,160723,171091,178183,192799,196543,200323,211879,219763

%N Primes p such that 2*p + 43 is a square.

%C Primes of the form 2*k^2 + 2*k - 21.

%t Select[Prime[Range[25000]], IntegerQ[Sqrt[2 # + 43]] &]

%o (Magma) [p: p in PrimesUpTo(300000) | IsSquare(2*p + 43)];

%o (PARI) lista(nn) = forprime(p=2, nn, if (issquare(2*p+43), 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+43)):continue

%o elif(is_prime(p)):print(p)

%o # _Soumil Mandal_, Apr 07 2016

%Y Cf. A000040.

%Y Subsequence of A002145, A045409.

%Y Cf. similar sequences listed in A269784.

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Mar 22 2016