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Primes p such that 2*p + 59 is a square.
1

%I #13 Sep 08 2022 08:46:16

%S 11,31,83,151,191,283,811,983,1171,1483,1831,2083,2351,3251,3583,3931,

%T 4111,4483,4871,5483,6131,8291,9631,11071,12611,14251,14591,15991,

%U 18211,20983,24391,27583,29983,30971,34031,35083,36151,36691,37783,38891,39451,40583

%N Primes p such that 2*p + 59 is a square.

%C Primes of the form 2*k^2 + 2*k - 29.

%e a(1) = 11 because 2*11 + 59 = 81, which is a square.

%t Select[Prime[Range[4500]], IntegerQ[Sqrt[2 # + 59]] &]

%o (Magma) [p: p in PrimesUpTo(50000) | IsSquare(2*p+59)];

%o (PARI) lista(nn) = {forprime(p=2, nn, if(issquare(2*p + 59), print1(p, ", "))); } \\ _Altug Alkan_, Mar 24 2016

%Y Cf. A000040.

%Y Subsequence of A002144, A045429.

%Y Cf. similar sequences listed in A269784.

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Mar 24 2016