A200816 Numbers k such that (2^k - k)*2^k + 1 is prime.

1, 3, 4, 10, 11, 16, 47, 57, 69, 166, 327, 460, 1108, 4740, 20760, 21143, 27779, 34293, 34311, 100590

Offset

1,2

Comments

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..20.

Henri Lifchitz, New forms of primes

Example

4 is in the sequence because (2^4 - 4)*2^4 + 1 = 193 is prime.

Mathematica

lst={}; Do[If[PrimeQ[(2^n - n)*2^n+1], AppendTo[lst, n]], {n, 10^3}]; lst

Prog

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

Crossrefs

Cf. A200817, A200818, A200819, A200821, A200822, A200823, A200832.

Sequence in context: A225571 A191134 A196101 * A327300 A047341 A091910

Adjacent sequences: A200813 A200814 A200815 * A200817 A200818 A200819

Keyword

nonn,more

Author

Michel Lagneau, Nov 23 2011

Extensions

a(17)-a(19) from Michael S. Branicky, Jul 14 2023

a(20) from Michael S. Branicky, May 03 2025

Status

approved