%I #32 Oct 09 2021 06:57:52

%S 3,7,11,23,47,59,71,79,83,103,107,127,131,139,151,163,167,179,191,199,

%T 211,227,239,251,263,271,283,311,331,347,359,367,383,419,431,439,443,

%U 463,467,479,487,499,503,523,547,563,571,587,599,607,647,659,691,719,727

%N Primes p for which the average of the primitive roots is > p/2.

%C It appears that these primes are all congruent to 3 (mod 4).

%H Amiram Eldar, <a href="/A267009/b267009.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = prime(A266990(n)).

%e a(2) = 7 since the primitive roots of 7 are 3 and 5 and their average is (3+5)/2 = 8/2 > 7/2.

%t A = Table[Total[Flatten[Position[Table[MultiplicativeOrder[i, Prime[k]], {i, Prime[k] - 1}], Prime[k] - 1]]]/(EulerPhi[Prime[k] - 1] Prime[k]/2), {k, 1, 1000}]; Prime[Flatten[Position[A, _?(# > 1 &)]]]

%t Select[Range[1000], PrimeQ[#] && Mean[PrimitiveRootList[#]] > #/2 &] (* _Amiram Eldar_, Oct 09 2021 *)

%Y Cf. A008330, A060749, A088144, A266990.

%K nonn

%O 1,1

%A _Dimitri Papadopoulos_, Jan 08 2016