A200817 Primes of the form (2^n - n)*2^n + 1.

2, 3, 41, 193, 1038337, 4171777, 4293918721, 19807040628559469736433287169, 20769187434139302299556264993095681, 348449143727040986545765187095379958562817

Offset

1,1

Comments

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

The corresponding n are in A200816.

For n = 166, a(10) has 100 digits; for n = 327, a(11) has 197 digits; for n = 460, a(12) has 277 digits; for n = 1108, a(13) has 668 digits; for n = 4740, a(14) has 2854 digits; for n = 20760, a(15) has 12499 digits; for n = 21143, a(16) has 12730 digits.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..14

Henri Lifchitz, De nouvelles formes de nombres premiers.

Example

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

Mathematica

a={}; Do[p=(2^n - n)*2^n + 1; If[PrimeQ[p], AppendTo[a, p]], {n, 5000}]; Print[a]
Select[Table[(2^n - n) 2^n + 1, {n, 0, 200}], PrimeQ] (* Vincenzo Librandi, Mar 15 2013 *)

Prog

(Magma) [a: n in [0..200] | IsPrime(a) where a is (2^n-n)*2^n+1]; // Vincenzo Librandi, Mar 15 2013

Crossrefs

Cf. A200816, A200818, A200819, A200821, A200822, A200823, A200832.

Sequence in context: A215154 A215101 A094714 * A042475 A241277 A123993

Adjacent sequences: A200814 A200815 A200816 * A200818 A200819 A200820

Keyword

nonn,easy

Author

Michel Lagneau, Nov 23 2011

Extensions

Added the term 2 from Vincenzo Librandi, Mar 15 2013

Status

approved