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a(n) is the smallest prime greater than 2^n such that 2 is a primitive root modulo a(n).
2

%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