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A019337 Primes with primitive root 7. 7

%I #36 Dec 03 2019 18:49:47

%S 2,5,11,13,17,23,41,61,67,71,79,89,97,101,107,127,151,163,173,179,211,

%T 229,239,241,257,263,269,293,347,349,359,379,397,431,433,443,461,491,

%U 499,509,521,547,577,593,599,601,631,659,677,683,733,739,743,761,773,797,823

%N Primes with primitive root 7.

%C To allow primes less than the specified primitive root m (here, 7) to be included, we use the essentially equivalent definition "Primes p such that the multiplicative order of m mod p is p-1". This comment applies to all of A019334-A019421. - _N. J. A. Sloane_, Dec 03 2019

%C All terms apart from the first are == 5, 11, 13, 15, 17, 23 (mod 28) since 7 is a quadratic residue modulo any other prime. By Artin's conjecture, this sequence contains about 37.395% of all primes, that is, about 74.79% of all primes == 5, 11, 13, 15, 17, 23 (mod 28). - _Jianing Song_, Sep 05 2018

%H Vincenzo Librandi, <a href="/A019337/b019337.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>

%t pr=7; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #-1 &]

%Y Cf. A167795.

%K nonn

%O 1,1

%A _David W. Wilson_

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Last modified April 16 00:00 EDT 2024. Contains 371696 sequences. (Running on oeis4.)