A266988 The indices of primes for which the average of the primitive roots is < p/2.

11, 14, 19, 48, 75, 94, 114, 115, 117, 124, 149, 153, 155, 177, 182, 224, 272, 300, 324, 348, 351, 365, 370, 403, 465, 510, 515, 522, 531, 546, 555, 578, 614, 634, 667, 677, 683, 707, 748, 765, 788, 795, 802, 808, 832, 850, 871, 876, 886, 888, 966, 980

Offset: 1

Author

Dimitri Papadopoulos, Jan 08 2016

Keywords

• nonn

Comments

These primes are all of the form p==3 (mod 4). (conjecture)

Examples

			p(a[1])=p(11)=31. The primitive roots of 31 are 3, 11, 12, 13, 17, 21, 22, and 24.
Their average is (3+11+12+13+17+21+22+24)/phi(30)=123/8<31/2.
		

Crossrefs

Cf. A008330, A060749, A088144, A266989.

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 &)]]