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A167791 Numbers with primitive root 2. 30

%I

%S 3,5,9,11,13,19,25,27,29,37,53,59,61,67,81,83,101,107,121,125,131,139,

%T 149,163,169,173,179,181,197,211,227,243,269,293,317,347,349,361,373,

%U 379,389,419,421,443,461,467,491,509,523,541,547,557,563,587,613,619

%N Numbers with primitive root 2.

%C Numbers n such that the binary expansion of 1/n has period phi(n). For example 1/27 has a period of 18 bits.

%C All entries are odd. An odd composite number n can have a primitive root if and only if it is a prime power (see A033948). - _V. Raman_, Oct 04 2012

%C It is unknown whether there is a prime p such that p is in this sequence while p^2 is not. - _Jianing Song_, Jan 27 2019

%H Vincenzo Librandi, <a href="/A167791/b167791.txt">Table of n, a(n) for n = 1..1000</a>

%t pr=2; Select[Range[2,2000], MultiplicativeOrder[pr,# ] == EulerPhi[ # ] &]

%o (PARI) for(n=3,200,if(n%2==1&&znorder(Mod(2,n))==eulerphi(n),printf(n","))) \\ _V. Raman_, Oct 04 2012

%o (PARI) is(n)=n%2 && isprimepower(n) && znorder(Mod(2,n))==eulerphi(n-1) \\ _Charles R Greathouse IV_, Jul 05 2013

%o (MAGMA) [n: n in [3..619] | IsPrimitive(2, n)]; // _Arkadiusz Wesolowski_, Dec 22 2020

%Y Cf. A001122 (primes with primitive root 2).

%K nonn

%O 1,1

%A _T. D. Noe_, Nov 12 2009

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Last modified April 12 10:52 EDT 2021. Contains 342920 sequences. (Running on oeis4.)