A200819 Primes of the form (2^k - k)*2^k - 1.

7, 191, 863, 63487, 22835963083295358096920939600178131376317399039

Offset

1,1

Comments

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

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

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

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

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

Links

Table of n, a(n) for n=1..5.

Henri Lifchitz, New forms of primes

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A010332 A368592 A198258 * A232146 A264353 A024096

Adjacent sequences: A200816 A200817 A200818 * A200820 A200821 A200822

Keyword

nonn,hard

Author

Michel Lagneau, Nov 23 2011

Extensions

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

Status

approved