A381590 Primes with primitive root -100.

3, 7, 19, 23, 31, 43, 47, 59, 67, 71, 83, 107, 131, 151, 163, 167, 179, 191, 199, 223, 227, 263, 283, 307, 311, 347, 359, 367, 379, 383, 419, 431, 439, 443, 467, 479, 487, 491, 499, 503, 523, 563, 571, 587, 599, 619, 631, 647, 659, 683, 719, 727, 743, 787, 811

Offset

1,1

Comments

Union of long period primes (A006883) of the form 4k-1 and half period primes (A097443) of the form 4k-1.

Complement of A007349 in the union of A007348 and A001913. - Davide Rotondo, May 23 2025

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

select(p -> isprime(p) and numtheory:-order(-100, p) = p-1, [seq(i, i=3..1000, 2)]); # Robert Israel, Oct 28 2025

Mathematica

Select[Prime[Range[150]], MultiplicativeOrder[-100, #] == # - 1 &]  (* Amiram Eldar, Mar 02 2025 *)

Prog

(PARI) is(n)=gcd(n, 10)==1 && znorder(Mod(-100, n))==n-1 \\ Charles R Greathouse IV, Mar 01 2025
(PARI) list(lim)=my(v=List([3])); forprime(p=7, lim, if(znorder(Mod(-100, p))==p-1, listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Mar 01 2025

Crossrefs

Cf. A006883, A097443, A007349, A007348, A001913.

Sequence in context: A248219 A322963 A018432 * A205302 A127925 A032388

Adjacent sequences: A381587 A381588 A381589 * A381591 A381592 A381593

Keyword

nonn,easy

Author

Davide Rotondo, Feb 28 2025

Status

approved