A377177 Primes p such that -7/2 is a primitive root modulo p.

11, 17, 29, 31, 37, 41, 43, 47, 73, 89, 103, 107, 109, 149, 167, 179, 197, 257, 277, 311, 313, 317, 347, 353, 367, 373, 383, 389, 409, 433, 479, 491, 499, 503, 521, 541, 557, 571, 577, 593, 601, 607, 647, 653, 659, 683, 701, 719, 727, 761, 769, 821, 839, 857, 883, 887, 907, 929, 937, 947, 983

Offset

1,1

Comments

If p is a term in this sequence, then -7/2 is not a square modulo p (i.e., p is in A191061).

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

Links

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

Wikipedia, Artin's conjecture on primitive roots.

Index entries for primes by primitive root

Maple

select(p -> isprime(p) and numtheory:-order(-7/2 mod p, p) = p-1, [seq(i, i=3..1000, 2)]); # Robert Israel, Nov 10 2024

Mathematica

Cases[Prime[Range[2, 170]], _?(MemberQ[PrimitiveRootList[#], ResourceFunction["FractionMod"][-7/2, #]]&)] (* Shenghui Yang, Oct 23 2024 *)

Prog

(PARI) forprime(p=8, 10^3, if(znorder(Mod(-7/2, p))==p-1, print1(p, ", "))); \\ Joerg Arndt, Oct 19 2024

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), this sequence (a=7), A377179 (a=9).

Cf. A191061, A005596.

Sequence in context: A079367 A120139 A191061 * A110055 A240095 A105886

Adjacent sequences: A377174 A377175 A377176 * A377178 A377179 A377180

Keyword

nonn,easy

Author

Jianing Song, Oct 18 2024

Status

approved