A200822 - OEIS

%I #23 Jun 07 2021 01:12:50

%S 5,23,295147905763468378111,

%T 26328072917139296674479506920934969822344499680020176660678574079

%N Primes of the form (2^k + k)*2^k - 1.

%C The corresponding indices k are 1, 2, 34, 107, 1568, 1933, 3551, 6793, ... (see A200821).

%C The generalization of this sequence is possible with the primes of the form  (b^n +- k)*b^n +- 1.

%C For k = 107, a(4) has 65 digits;

%C for k = 1568, a(5) has 945 digits;

%C for k = 1933, a(6) has 1164 digits;

%C for k = 3551, a(7) has 2138 digits;

%C for k = 6793, a(8) has 4090 digits.

%H Henri Lifchitz, <a href="http://www.primenumbers.net/Henri/us/NouvP1us.htm">New forms of primes</a>

%e 23 is in the sequence because, for k=2, (2^2 + 2)*2^2 - 1 = 23 is prime.

%t a={}; Do[p=(2^n + n)*2^n-1; If[PrimeQ[p], AppendTo[a, p]], {n, 10^3}]; Print[a]

%t Select[Table[(2^n+n)2^n-1,{n,200}],PrimeQ] (* _Harvey P. Dale_, Dec 18 2015 *)

%Y Cf. A200816, A200817, A200818, A200819, A200821, A200823, A200832.

%K nonn

%O 1,1

%A _Michel Lagneau_, Nov 23 2011