A392947 - OEIS

%I #30 Feb 06 2026 16:30:49

%S 5,13,17,29,37,41,53,61,97,101,109,113,137,149,157,173,181,193,197,

%T 229,241,257,269,277,293,313,317,349,353,373,389,397,401,409,421,433,

%U 449,457,461,509,521,541,557,569,577,593,613,641,653,661,673,677,701,709

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

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

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

%C Together with 3, supersequence of A023394.

%H Arkadiusz Wesolowski, <a href="/A392947/b392947.txt">Table of n, a(n) for n = 1..10000</a>

%H Tuvi Etzion, <a href="https://doi.org/10.1016/0097-3165(92)90069-7">Partitions of triples into optimal packings</a>, Journal of Combinatorial Theory, Series A 59, (1992). See p. 281.

%H Shmuel Schreiber, <a href="https://doi.org/10.1016/0012-365X(89)90367-1">Symmetric quasigroups of odd order</a>, Discrete Math. 77 (1989), pp. 287-288.

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

%o (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))];

%o (PARI) isok(p) = p>2 && isprime(p) && !(znorder(Mod(-2, p))%4);

%Y Complement in odd primes of (A014663 union A163183).

%Y Cf. A007519, A007521, A023394.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Jan 27 2026