A377179 - OEIS

A377179

Primes p such that -9/2 is a primitive root modulo p.

5, 13, 23, 29, 31, 47, 53, 61, 71, 79, 101, 109, 149, 151, 157, 167, 173, 191, 197, 199, 223, 229, 239, 263, 269, 277, 293, 311, 317, 359, 367, 373, 383, 389, 461, 463, 479, 487, 503, 509, 557, 599, 613, 647, 653, 661, 677, 701, 709, 719, 733, 743, 757, 773, 797, 821, 823, 829, 839, 853, 863, 887, 911, 967, 983, 991

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OFFSET

1,1

COMMENTS

If p is a term in this sequence, then -9/2 is not a square modulo p (i.e., p is in A003628).

Conjecture: this sequence has relative density equal to Artin's constant (A005596) with respect to the set of primes.

LINKS

Table of n, a(n) for n=1..66.

Wikipedia, Artin's conjecture on primitive roots.

Index entries for primes by primitive root

PROG

(PARI) forprime(p=5, 10^3, if(znorder(Mod(-9/2, p))==p-1, print1(p, ", ")));

CROSSREFS

Primes p such that +a/2 is a primitive root modulo p: A320384 (a=3), A377174 (a=5), A377176 (a=7), A377178 (a=9).

Primes p such that -a/2 is a primitive root modulo p: A377172 (a=3), A377175 (a=5), A377177 (a=7), this sequence (a=9).

Cf. A003628, A005596.

Sequence in context: A076408 A006353 A155142 * A155552 A219546 A143988

Adjacent sequences: A377176 A377177 A377178 * A377180 A377181 A377182

KEYWORD

nonn,easy

AUTHOR

Jianing Song, Oct 18 2024

STATUS

approved