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 A385220 #22 Jun 28 2025 12:53:34
%S A385220 2,11,13,23,47,59,71,83,107,109,131,167,179,181,191,227,229,239,251,
%T A385220 263,277,311,313,347,359,383,419,421,431,433,443,467,479,491,503,541,
%U A385220 563,587,599,601,647,659,683,709,719,733,743,757,827,829,839,863,887,911,947,971,983
%N A385220 Primes p such that multiplicative order of 3 modulo p is odd.
%C A385220 The multiplicative order of 3 modulo a(n) is A385226(n).
%C A385220 Without 2, contained in primes congruent to 1 or 11 modulo 12 (primes p such that 3 is a quadratic residue modulo p; A097933), and contains primes congruent to 11 modulo 12 (A068231).
%C A385220 Conjecture: this sequence has density 1/3 among the primes.
%H A385220 Jianing Song, <a href="/A385220/b385220.txt">Table of n, a(n) for n = 1..10000</a>
%t A385220 Select[Prime[Range[200]], OddQ[MultiplicativeOrder[3, #]] &] (* _Paolo Xausa_, Jun 28 2025 *)
%o A385220 (PARI) isA385220(p) = isprime(p) && (p!=3) && znorder(Mod(3,p))%2
%Y A385220 A068231 < this sequence < A045317 < A040101 < A097933 (ignoring terms 2, 3), where Ax < Ay means that Ax is a subsequence of Ay.
%Y A385220 Complement of A301916 in {primes} \ {3}.
%Y A385220 Cf. A385226 (the actual multiplicative orders).
%Y A385220 Cf. other bases: A014663 (base 2), this sequence (base 3), A385221 (base 4), A385192 (base 5), A163183 (base -2), A385223 (base -3), A385224 (base -4), A385225 (base -5).
%K A385220 nonn,easy
%O A385220 1,1
%A A385220 _Jianing Song_, Jun 22 2025