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Numbers k such that 23*k^2 + 16 is prime.
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%I #15 Sep 08 2022 08:45:20

%S 3,9,21,45,63,69,81,93,123,135,141,153,165,201,219,231,243,267,273,

%T 279,309,327,381,471,477,513,525,531,543,555,561,579,585,591,603,621,

%U 645,657,669,687,693,717,723,741,759,765,801,825,861,873,879,903,915,933

%N Numbers k such that 23*k^2 + 16 is prime.

%H Emre Alkan, Alexandru Zaharescu, <a href="https://doi.org/10.1142/S1793042105000029">Nonvanishing of the Ramanujan tau function in short intervals</a>, International Journal of Number Theory, Vol. 1, No. 1 (2005) 45-51.

%e 23*135^2 + 16 = 419191 (prime).

%o (Magma) [ n: n in [0..1500] | IsPrime( 23*n^2 + 16) ] // _Vincenzo Librandi_, Jan 31 2011

%o (PARI) is(n)=isprime(23*n^2+16) \\ _Charles R Greathouse IV_, Jun 13 2017

%K nonn,easy

%O 1,1

%A _Parthasarathy Nambi_, Sep 26 2005

%E Edited by _Don Reble_, Nov 08 2005