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%I #16 Apr 24 2019 06:11:13
%S 11,61,101,131,181,211,421,461,491,541,661,701,821,941,1061,1091,1171,
%T 1291,1301,1381,1451,1531,1571,1621,1741,1861,1901,1931,2131,2141,
%U 2221,2371,2531,2621,2741,2851,2861,3011,3371,3461,3491,3571,3581,3691,3701,3851,3931
%N Primes p such that 2 is a primitive root modulo p while 32 is not.
%C Primes p such that 2 is a primitive root modulo p (i.e., p is in A001122) and that p == 1 (mod 5).
%C By Artin's conjecture, the number of terms <= N is roughly ((4/19)*C)*PrimePi(N), where C is the Artin's constant = A005596, PrimePi = A000720. Compare: the number of terms of A001122 that are no greater than N is roughly C*PrimePi(N).
%H Robert Israel, <a href="/A307628/b307628.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ArtinsConstant.html">Artin's constant</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots">Artin's conjecture on primitive roots</a>
%e For p = 61, the multiplicative order of 2 modulo 61 is 60, while 32^12 == 2^(5*12) == 1 (mod 61), so 61 is a term.
%p select(p -> isprime(p) and numtheory:-order(2,p) = p-1,
%p [seq(i,i=1..10000,10)]); # _Robert Israel_, Apr 23 2019
%t {11}~Join~Select[Prime@ Range[11, 550], And[FreeQ[#, 32], ! FreeQ[#, 2]] &@ PrimitiveRootList@ # &] (* _Michael De Vlieger_, Apr 23 2019 *)
%o (PARI) forprime(p=3, 4000, if(znorder(Mod(2, p))==(p-1) && p%5==1, print1(p, ", ")))
%Y Complement of A019358 with respect to A001122.
%Y Cf. also A005596, A000720, A307627.
%K nonn
%O 1,1
%A _Jianing Song_, Apr 19 2019
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