A356856 - OEIS

%I #13 Aug 31 2023 14:58:48

%S 2,3,5,7,11,13,19,29,31,37,43,53,59,61,67,71,79,83,101,107,109,127,

%T 131,139,149,151,163,173,179,181,191,197,199,211,223,227,229,239,269,

%U 271,283,293,317,331,347,349,367,373,379,389,419,421,443,461,463,467,487

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

%C If Artin's conjecture is true then this sequence is infinite because it contains all primes with primitive root 2.

%C Conjecture: This sequence has density ~0.548 in the prime numbers.

%H Robert Israel, <a href="/A356856/b356856.txt">Table of n, a(n) for n = 1..10000</a>

%e 71 is a term because the least primitive root of the prime number 71 is 7 and 7 divides 71 - 1 = 70.

%p filter:= proc(p) local r;

%p   if not isprime(p) then return false fi;

%p   r:= NumberTheory:-PrimitiveRoot(p);

%p   p-1 mod r = 0

%p end proc:

%p select(filter, [2,seq(i,i=3..1000,2)]); # _Robert Israel_, Aug 31 2023

%t Select[Prime@Range@100, Mod[# - 1, PrimitiveRoot@#] == 0 &]

%Y Cf. A006093, A001918.

%K nonn

%O 1,1

%A _Giorgos Kalogeropoulos_, Aug 31 2022