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A377177
Primes p such that -7/2 is a primitive root modulo p.
6
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.
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).
Sequence in context: A079367 A120139 A191061 * A110055 A240095 A105886
KEYWORD
nonn,easy,new
AUTHOR
Jianing Song, Oct 18 2024
STATUS
approved