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A363286 Odd primes p such that the congruence 2^x == 1 (mod p) has no solution for 0 < x < (p - 1)/2.

%I A363286 #11 Jul 17 2023 09:03:29
%S A363286 3,5,7,11,13,17,19,23,29,37,41,47,53,59,61,67,71,79,83,97,101,103,107,
%T A363286 131,137,139,149,163,167,173,179,181,191,193,197,199,211,227,239,263,
%U A363286 269,271,293,311,313,317,347,349,359,367,373,379,383,389,401,409,419
%N A363286 Odd primes p such that the congruence 2^x == 1 (mod p) has no solution for 0 < x < (p - 1)/2.
%C A363286 An odd prime p belongs to this sequence if and only if A001917(A000720(p)) is equal to 1 or 2.
%F A363286 a(n) ~ (3/2)*n*log((3/2)*n).
%o A363286 (Magma) [p: p in [3..419 by 2] | IsPrime(p) and (p-1)/Modorder(2, p) le 2];
%o A363286 (PARI) isok(p) = p%2 && isprime(p) && (p-1)/znorder(Mod(2, p))<=2;
%o A363286 (Python)
%o A363286 from itertools import islice
%o A363286 from sympy import nextprime, n_order
%o A363286 def A363286_gen(startvalue=3): # generator of terms >= startvalue
%o A363286     p = max(startvalue,3)-1
%o A363286     while (p:=nextprime(p)):
%o A363286         if n_order(2,p)<<1 >= p-1:
%o A363286             yield p
%o A363286 A363286_list = list(islice(A363286_gen(),30)) # _Chai Wah Wu_, Jul 17 2023
%Y A363286 Cf. A001917, A014664.
%K A363286 nonn
%O A363286 1,1
%A A363286 _Arkadiusz Wesolowski_, May 25 2023