A377172 Primes p such that -3/2 is a primitive root modulo p.

17, 23, 37, 41, 43, 47, 67, 89, 109, 113, 137, 139, 157, 163, 167, 191, 229, 233, 239, 257, 263, 277, 283, 311, 349, 353, 359, 379, 383, 397, 421, 449, 479, 503, 521, 523, 541, 547, 569, 571, 593, 599, 613, 619, 641, 647, 661, 719, 733, 739, 743, 757, 761, 787, 809, 811, 839, 853, 857, 859, 863, 877, 887, 911, 929, 953, 977, 983

Offset

1,1

Comments

If p is a term in this sequence, then -3/2 is not a square modulo p (i.e., p is in A191059).

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..68.

Wikipedia, Artin's conjecture on primitive roots.

Index entries for primes by primitive root

Prog

(PARI) forprime(p=5, 10^3, if(znorder(Mod(-3/2, 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: this sequence (a=3), A377175 (a=5), A377177 (a=7), A377179 (a=9).

Cf. A191059, A005596.

Sequence in context: A080830 A165566 A072184 * A107644 A158710 A103805

Adjacent sequences: A377169 A377170 A377171 * A377173 A377174 A377175

Keyword

nonn,easy

Author

Jianing Song, Oct 18 2024

Status

approved