A392947 Primes p such that the multiplicative order of -2 modulo p is a multiple of 4.

5, 13, 17, 29, 37, 41, 53, 61, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 241, 257, 269, 277, 293, 313, 317, 349, 353, 373, 389, 397, 401, 409, 421, 433, 449, 457, 461, 509, 521, 541, 557, 569, 577, 593, 613, 641, 653, 661, 673, 677, 701, 709

Offset

1,1

Comments

Sequence contains all primes of the form 8*k + 5 (A007521) and some primes of the form 8*k + 1 (A007519).

Primes dividing 2^m + 1 only for some even values of m.

Together with 3, supersequence of A023394.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Tuvi Etzion, Partitions of triples into optimal packings, Journal of Combinatorial Theory, Series A 59, (1992). See p. 281.

Shmuel Schreiber, Symmetric quasigroups of odd order, Discrete Math. 77 (1989), pp. 287-288.

Mathematica

okQ[k_]:=Divisible[MultiplicativeOrder[-2, k], 4]; Select[Prime[Range[127]], okQ] (* James C. McMahon, Feb 06 2026 *)

Prog

(Magma) [p: p in PrimesInInterval(3, 709) | p mod 8 eq 5 or (p mod 8 eq 1 and IsZero(Modorder(-2, p) mod 4))];
(PARI) isok(p) = p>2 && isprime(p) && !(znorder(Mod(-2, p))%4);

Crossrefs

Complement in odd primes of (A014663 union A163183).

Cf. A007519, A007521, A023394.

Sequence in context: A192592 A357218 A349900 * A347163 A111055 A307096

Adjacent sequences: A392944 A392945 A392946 * A392948 A392949 A392950

Keyword

nonn

Author

Arkadiusz Wesolowski, Jan 27 2026

Status

approved