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%I A035089 #43 Jun 21 2023 12:06:55
%S A035089 2,3,5,17,17,97,193,257,257,7681,12289,12289,12289,40961,65537,65537,
%T A035089 65537,786433,786433,5767169,7340033,23068673,104857601,167772161,
%U A035089 167772161,167772161,469762049,2013265921,3221225473,3221225473,3221225473,75161927681
%N A035089 Smallest prime of form 2^n*k + 1.
%C A035089 a(n) is the smallest prime p such that the multiplicative group modulo p has a subgroup of order 2^n. - _Joerg Arndt_, Oct 18 2020
%H A035089 Alois P. Heinz, <a href="/A035089/b035089.txt">Table of n, a(n) for n = 0..1000</a>
%H A035089 Gareth A. Jones and Alexander K. Zvonkin, <a href="https://www.labri.fr/perso/zvonkin/Research/ProjPrimesShort.pdf">Groups of prime degree and the Bateman-Horn conjecture</a>, 2021.
%t A035089 a = {}; Do[k = 0; While[ !PrimeQ[k 2^n + 1], k++ ]; AppendTo[a, k 2^n + 1], {n, 1, 50}]; a (* _Artur Jasinski_ *)
%o A035089 (PARI) a(n)=for(k=1,9e99,if(ispseudoprime(k<<n+1),return(k<<n+1))) \\ _Charles R Greathouse IV_, Jul 06 2011
%Y A035089 Analogous case is A034694. Fermat primes (A019434) are a subset. See also Fermat numbers A000215.
%Y A035089 Cf. A007522, A057775, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587.
%K A035089 nonn
%O A035089 0,1
%A A035089 _Labos Elemer_
%E A035089 a(0) from _Joerg Arndt_, Jul 06 2011

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