A377178 Primes p such that 9/2 is a primitive root modulo p.

5, 13, 19, 29, 43, 53, 59, 61, 83, 101, 107, 109, 149, 157, 173, 179, 197, 227, 229, 251, 269, 277, 283, 293, 317, 331, 347, 373, 389, 419, 443, 461, 467, 491, 509, 523, 547, 557, 563, 587, 613, 619, 653, 661, 677, 683, 691, 701, 709, 733, 739, 757, 773, 787, 797, 821, 829, 853, 883, 907, 947, 971

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 A003629).

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..62.

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), this sequence (a=9).

Primes p such that -a/2 is a primitive root modulo p: A377172 (a=3), A377175 (a=5), A377177 (a=7), A377179 (a=9).

Cf. A003629, A005596.

Sequence in context: A287615 A129919 A045454 * A356833 A166575 A265808

Adjacent sequences: A377175 A377176 A377177 * A377179 A377180 A377181

Keyword

nonn,easy

Author

Jianing Song, Oct 18 2024

Status

approved