A267009 Primes p for which the average of the primitive roots is > p/2.

3, 7, 11, 23, 47, 59, 71, 79, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 227, 239, 251, 263, 271, 283, 311, 331, 347, 359, 367, 383, 419, 431, 439, 443, 463, 467, 479, 487, 499, 503, 523, 547, 563, 571, 587, 599, 607, 647, 659, 691, 719, 727

Offset

1,1

Comments

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

Links

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

Formula

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

Example

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

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}]; Prime[Flatten[Position[A, _?(# > 1 &)]]]
Select[Range[1000], PrimeQ[#] && Mean[PrimitiveRootList[#]] > #/2 &] (* Amiram Eldar, Oct 09 2021 *)

Crossrefs

Cf. A008330, A060749, A088144, A266990.

Sequence in context: A284402 A284543 A267052 * A116606 A188132 A139814

Adjacent sequences: A267006 A267007 A267008 * A267010 A267011 A267012

Keyword

nonn

Author

Dimitri Papadopoulos, Jan 08 2016

Status

approved