Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #19 Oct 07 2021 01:59:11
%S 3,3,5,11,19,37,67,131,269,523,1061,2053,4099,8219,16421,32771,65539,
%T 131213,262147,524309,1048589,2097211,4194371,8388619,16777259,
%U 33554467,67108933,134217773,268435459,536871019,1073741827,2147483659,4294967357,8589934621,17179869269,34359738421,68719476851,137438953741
%N a(n) is the smallest prime greater than 2^n such that 2 is a primitive root modulo a(n).
%D Henri Cohen, A Course in Computational Algebraic Number Theory, Springer Verlag, (1993)
%H Amiram Eldar, <a href="/A250396/b250396.txt">Table of n, a(n) for n = 0..300</a>
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational; Ideas, Algorithms, Source Code</a>, (ยง1.5.1, p.13).
%t With[{n = 20},
%t Module[{p = NextPrime[2^n]},
%t While[FreeQ[PrimitiveRootList[p], 2], p = NextPrime[p]]; p]]
%o (PARI) a(n)=forprime(p=2^n+1,,if(znorder(Mod(2,p))==p-1,return(p))); \\ _Joerg Arndt_, Nov 21 2014
%Y Cf. A104080 (smallest prime >= 2^n).
%K nonn
%O 0,1
%A _Morgan L. Owens_, Nov 21 2014