A200818 Numbers k such that (2^k - k)*2^k - 1 is prime.

2, 4, 5, 8, 77, 377, 4547, 8248, 27502

Offset

1,1

Comments

No more terms < 17000. - L. Joris Perrenet, Mar 17 2020

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

Links

Table of n, a(n) for n=1..9.

Henri Lifchitz, New forms of primes

Example

4 is in the sequence because (2^4 - 4)*2^4 - 1 = 191 is prime.

Mathematica

lst={}; Do[If[PrimeQ[(2^n - n)*2^n-1], AppendTo[lst, n]], {n, 10^3}]; lst
Select[Range[8300], PrimeQ[(2^#-#)2^#-1]&] (* The program generates the first 8 terms of the sequence. *) (* Harvey P. Dale, Aug 31 2024 *)

Prog

(PARI) is(n)=ispseudoprime((2^n-n)<<n-1) \\ Charles R Greathouse IV, Feb 17 2017

Crossrefs

Cf. A200816, A200817, A200819, A200821, A200822, A200823, A200832.

Sequence in context: A013154 A013129 A104311 * A021980 A303496 A169624

Adjacent sequences: A200815 A200816 A200817 * A200819 A200820 A200821

Keyword

nonn,hard,more

Author

Michel Lagneau, Nov 23 2011

Extensions

a(8) from L. Joris Perrenet, Mar 17 2020

a(9) from Michael S. Branicky, Jul 14 2023

Status

approved