A200822 Primes of the form (2^k + k)*2^k - 1.

5, 23, 295147905763468378111, 26328072917139296674479506920934969822344499680020176660678574079

Offset

1,1

Comments

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

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

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

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

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

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

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

Links

Table of n, a(n) for n=1..4.

Henri Lifchitz, New forms of primes

Example

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

Mathematica

a={}; Do[p=(2^n + n)*2^n-1; If[PrimeQ[p], AppendTo[a, p]], {n, 10^3}]; Print[a]
Select[Table[(2^n+n)2^n-1, {n, 200}], PrimeQ] (* Harvey P. Dale, Dec 18 2015 *)

Crossrefs

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

Sequence in context: A174106 A120660 A110720 * A112613 A305057 A333633

Adjacent sequences: A200819 A200820 A200821 * A200823 A200824 A200825

Keyword

nonn

Author

Michel Lagneau, Nov 23 2011

Status

approved