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A200817 Primes of the form (2^n - n)*2^n + 1. 8

%I #20 Sep 08 2022 08:46:00

%S 2,3,41,193,1038337,4171777,4293918721,19807040628559469736433287169,

%T 20769187434139302299556264993095681,

%U 348449143727040986545765187095379958562817

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

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

%C The corresponding n are in A200816.

%C 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.

%H Vincenzo Librandi, <a href="/A200817/b200817.txt">Table of n, a(n) for n = 1..14</a>

%H Henri Lifchitz, <a href="http://www.primenumbers.net/Henri/fr/NouvP1.htm">De nouvelles formes de nombres premiers</a>.

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

%t a={}; Do[p=(2^n - n)*2^n + 1; If[PrimeQ[p], AppendTo[a, p]], {n, 5000}]; Print[a]

%t Select[Table[(2^n - n) 2^n + 1, {n, 0, 200}], PrimeQ] (* _Vincenzo Librandi_, Mar 15 2013 *)

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

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

%K nonn,easy

%O 1,1

%A _Michel Lagneau_, Nov 23 2011

%E Added the term 2 from _Vincenzo Librandi_, Mar 15 2013

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)