A266990 The indices of primes p for which the average of the primitive roots is > p/2.

2, 4, 5, 9, 15, 17, 20, 22, 23, 27, 28, 31, 32, 34, 36, 38, 39, 41, 43, 46, 47, 49, 52, 54, 56, 58, 61, 64, 67, 69, 72, 73, 76, 81, 83, 85, 86, 90, 91, 92, 93, 95, 96, 99, 101, 103, 105, 107, 109, 111, 118, 120, 125, 128, 129, 131, 132, 133, 138, 141, 143, 144, 146, 150

Offset: 1

Author

Dimitri Papadopoulos, Jan 08 2016

Keywords

• nonn

Comments

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

Examples

			a(2) = 4 is a term since prime(a(2)) = prime(4) = 7, the primitive roots of 7 are 3 and 5 and their average is (3+5)/2 = 8/2 > 7/2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A008330, A060749, A088144, A267009.

Programs

Mathematica

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}]; Flatten[Position[A, _?(# > 1 &)]]
Select[Range[150], Mean[PrimitiveRootList[(p = Prime[#])]] > p/2 &] (* Amiram Eldar, Oct 09 2021 *)

Formula

a(n) = A000720(A267009(n)). - Amiram Eldar, Oct 09 2021