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Primes of the form (2^k - k)*2^k - 1.
7

%I #27 Jun 07 2021 01:13:12

%S 7,191,863,63487,22835963083295358096920939600178131376317399039

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

%C The corresponding indices k are 2, 4, 5, 8, 77, 377, 4547, ... (see A200818).

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

%C For k = 377, a(6) contains 227 digits;

%C For k = 4547, a(7) contains 2738 digits;

%C For k = 8248, a(8) contains 4966 digits.

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

%e 191 is in the sequence because, for k=4, (2^4 - 4)*2^4 - 1 = 191 is prime.

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

%Y Cf. A200816, A200817, A200818, A200821, A200822, A200823, A200832.

%K nonn,hard

%O 1,1

%A _Michel Lagneau_, Nov 23 2011

%E a(8) from _L. Joris Perrenet_, Mar 17 2020