A200823 Numbers k such that (2^k + k)*2^k + 1 is prime.

1, 3, 6, 14, 21, 27, 51, 61, 103, 123, 126, 414, 499, 1509, 2389, 5973, 8558, 12673

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..18.

Henri Lifchitz, New forms of primes

Example

3 is in the sequence because (2^3 + 3)*2^3 + 1 = 89 is prime.

Mathematica

lst={}; Do[If[PrimeQ[(2^n + n)*2^n+1], AppendTo[lst, n]], {n, 5000}]; lst

Prog

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

Crossrefs

Cf. A200816, A200817, A200818, A200819, A200821, A200822, A200832.

Sequence in context: A109757 A075189 A291987 * A093866 A056596 A026341

Adjacent sequences: A200820 A200821 A200822 * A200824 A200825 A200826

Keyword

nonn,more

Author

Michel Lagneau, Nov 23 2011

Extensions

a(16)-a(18) from Michael S. Branicky, Jul 13 2023

Status

approved