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 A234972 Least prime p < prime(n) such that 2^p - 1 is a primitive root modulo prime(n), or 0 if such a prime p does not exist. 9

%I #19 Jul 26 2014 05:08:42

%S 0,0,2,2,3,3,2,2,3,2,2,17,3,2,5,2,5,3,3,3,5,2,11,2,3,2,13,3,7,2,2,5,2,

%T 2,2,3,11,2,11,2,3,7,7,7,2,2,2,2,5,3,2,3,3,7,2,3,2,11,5,2,2,2,5,5,5,2,

%U 2,5,3,3,2,3,7,7,2,7,2,3,2,7,5,31,3,3,5,3,2,5,2,2,5,5,2,3,3,5,2,2,7,7

%N Least prime p < prime(n) such that 2^p - 1 is a primitive root modulo prime(n), or 0 if such a prime p does not exist.

%C Conjecture: a(n) > 0 for all n > 2.

%H Zhi-Wei Sun, <a href="/A234972/b234972.txt">Table of n, a(n) for n = 1..2000</a>

%e a(3) = 2 since 2 is a prime smaller than prime(3) = 5 with 2^2 - 1 = 3 a primitive root modulo prime(3) = 5.

%t gp[g_,p_]:=Mod[g,p]>0&&(Length[Union[Table[Mod[g^k, p],{k,1,p-1}]]]==p-1)

%t Do[Do[If[gp[2^(Prime[k])-1,Prime[n]],Print[n," ",Prime[k]];Goto[aa]],{k,1,n-1}];Print[n," ",0];Label[aa];Continue,{n,1,100}]

%Y Cf. A000040, A001348, A001918.

%K nonn

%O 1,3

%A _Zhi-Wei Sun_, Apr 20 2014

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Last modified February 29 09:21 EST 2024. Contains 370418 sequences. (Running on oeis4.)