A002263 - OEIS

%I M0721 N0269 #31 Sep 08 2022 08:44:30

%S 1,2,3,5,10,11,26,32,39,92,116,134,170,224,277,332,370,374,640,664,

%T 820,1657,1952,1969,2576

%N Numbers k such that 25*4^k + 1 is prime.

%D H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see pp. 381-384.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Ray Ballinger, <a href="http://www.prothsearch.com/index.html">Proth Search Page</a>

%H R. M. Robinson, <a href="https://doi.org/10.1090/S0002-9939-1958-0096614-7">A report on primes of the form k.2^n+1 and on factors of Fermat numbers</a>, Proc. Amer. Math. Soc., 9 (1958), 673-681.

%t Select[Range[0, 4000], PrimeQ[(25 4^# + 1)] &] (* _Vincenzo Librandi_, Sep 07 2012 *)

%o (Magma) [n: n in [0..3000] | IsPrime(25*4^n + 1)]; // _Vincenzo Librandi_, Sep 07 2012

%o (PARI) is(n)=ispseudoprime(25*4^n+1) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y For more terms see A032362.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E a(25) from _Vincenzo Librandi_, Sep 07 2012