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Numbers k such that 4^k - 5 is prime.
2

%I #20 Nov 28 2023 16:53:40

%S 2,3,4,5,6,9,10,13,16,18,28,33,59,65,75,83,103,113,275,353,405,568,

%T 614,909,1184,1200,1564,2266,2556,4246,8014,8193,8696,9291,10993,

%U 12146,13809,15459,16381,24106,60220,91816,158070,182491,207016,266675,297561

%N Numbers k such that 4^k - 5 is prime.

%F a(n) = A059608(n+1)/2. - _Daniel Starodubtsev_, Mar 20 2020

%e 28 is a term because 4^28 - 5 = 72057594037927931 is prime.

%t Select[Range[10000], PrimeQ[4^# - 5] &]

%o (PARI) /* Up to 620 the code produces in few seconds the first terms: */

%o allocatemem(10000000); for(n=2, 620, if(isprime(4^n-5), print1(n", ")));

%Y Cf. A059266, A059608, A059614.

%K nonn,more

%O 1,1

%A _Vincenzo Librandi_, Oct 01 2012

%E a(31)-a(34) from _Bruno Berselli_, Oct 02 2012

%E a(35)-a(45) from _Daniel Starodubtsev_, Mar 20 2020

%E a(46)-a(47) derived from A059608 by _Elmo R. Oliveira_, Nov 28 2023