A105877 Primes for which -5 is a primitive root.

2, 11, 17, 19, 37, 53, 59, 73, 79, 97, 113, 131, 137, 139, 151, 157, 173, 179, 193, 197, 233, 239, 257, 277, 293, 311, 317, 331, 353, 359, 373, 397, 419, 431, 433, 439, 479, 491, 499, 557, 571, 577, 593, 599, 613, 617, 619, 653, 659, 673, 677, 719, 751, 757, 773, 797, 811

Offset: 1

Author

N. J. A. Sloane, Apr 24 2005

Keywords

• nonn

Comments

Conjecture: the penultimate digit of a(n) is always odd. This characteristic seems to be proper of primes for which -5*n^2 is a primitive root. - Davide Rotondo, Oct 26 2024

For any n > 1, a(n) == 11, 13, 17, or 19 (mod 20), which implies the conjecture above. - Max Alekseyev, Nov 01 2024

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for primes by primitive root

Programs

Mathematica

pr=-5; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #-1 &]