This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385223 #21 Jun 28 2025 11:15:26 %S A385223 2,7,19,31,37,43,61,67,79,103,127,139,151,157,163,199,211,223,271,283, %T A385223 307,331,349,367,373,379,397,439,463,487,499,523,547,571,607,613,619, %U A385223 631,643,661,691,727,739,751,787,811,823,853,859,877,883,907,919,937,967,991,997 %N A385223 Primes p such that multiplicative order of -3 modulo p is odd. %C A385223 The multiplicative order of -3 modulo a(n) is A385229(n). %C A385223 Without 2, contained in primes congruent to 1 modulo 3 (primes p such that -3 is a quadratic residue modulo p, A002476), and contains primes congruent to 7 modulo 12 (A068229). %C A385223 Conjecture: this sequence has density 1/3 among the primes. %H A385223 Jianing Song, <a href="/A385223/b385223.txt">Table of n, a(n) for n = 1..10000</a> %t A385223 Select[Prime[Range[200]], OddQ[MultiplicativeOrder[-3, #]] &] (* _Paolo Xausa_, Jun 28 2025 *) %o A385223 (PARI) isA385223(p) = isprime(p) && (p!=3) && znorder(Mod(-3,p))%2 %Y A385223 Subsequence of A002476. Contains A068229 as a subsequence. %Y A385223 Cf. A385229 (the actual multiplicative orders). %Y A385223 Cf. other bases: A014663 (base 2), A385220 (base 3), A385221 (base 4), A385192 (base 5), A163183 (base -2), this sequence (base -3), A385224 (base -4), A385225 (base -5). %K A385223 nonn,easy %O A385223 1,1 %A A385223 _Jianing Song_, Jun 22 2025