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A356856 Primes p such that the least positive primitive root of p (A001918) divides p-1.

%I A356856 #13 Aug 31 2023 14:58:48
%S A356856 2,3,5,7,11,13,19,29,31,37,43,53,59,61,67,71,79,83,101,107,109,127,
%T A356856 131,139,149,151,163,173,179,181,191,197,199,211,223,227,229,239,269,
%U A356856 271,283,293,317,331,347,349,367,373,379,389,419,421,443,461,463,467,487
%N A356856 Primes p such that the least positive primitive root of p (A001918) divides p-1.
%C A356856 If Artin's conjecture is true then this sequence is infinite because it contains all primes with primitive root 2.
%C A356856 Conjecture: This sequence has density ~0.548 in the prime numbers.
%H A356856 Robert Israel, <a href="/A356856/b356856.txt">Table of n, a(n) for n = 1..10000</a>
%e A356856 71 is a term because the least primitive root of the prime number 71 is 7 and 7 divides 71 - 1 = 70.
%p A356856 filter:= proc(p) local r;
%p A356856   if not isprime(p) then return false fi;
%p A356856   r:= NumberTheory:-PrimitiveRoot(p);
%p A356856   p-1 mod r = 0
%p A356856 end proc:
%p A356856 select(filter, [2,seq(i,i=3..1000,2)]); # _Robert Israel_, Aug 31 2023
%t A356856 Select[Prime@Range@100, Mod[# - 1, PrimitiveRoot@#] == 0 &]
%Y A356856 Cf. A006093, A001918.
%K A356856 nonn
%O A356856 1,1
%A A356856 _Giorgos Kalogeropoulos_, Aug 31 2022