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Primes of the form 2*4^n - n.
0

%I #30 Sep 08 2022 08:46:09

%S 2,7,549755813869,2475880078570760549798248403

%N Primes of the form 2*4^n - n.

%C a(5) and a(6) are 125 and 266 decimal digits long, respectively. - _Derek Orr_, Aug 28 2014

%e 2*4^0 - 0 = 2 is prime, thus 2 is a member of this sequence.

%t Select[Table[2^(2n + 1) - n, {n, 0, 127}], PrimeQ] (* _Alonso del Arte_, Sep 16 2014 *)

%o (Magma) [a: n in [0..500] | IsPrime(a) where a is 2*4^n - n];

%o (PARI)

%o for(n=0,10^3,if(ispseudoprime(2^(2*n+1)-n),print1(2^(2*n+1)-n,", "))) \\ _Derek Orr_, Aug 28 2014

%Y Cf. A100362, A241861.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Aug 28 2014