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 A385192 #23 Jun 28 2025 12:53:24 %S A385192 2,11,19,31,59,71,79,101,109,131,139,149,151,179,181,191,199,211,239, %T A385192 251,269,271,311,331,359,379,389,401,409,419,431,439,461,479,491,499, %U A385192 541,569,571,599,619,631,659,691,719,739,751,811,829,839,859,911,919,941,971,991 %N A385192 Primes p such that multiplicative order of 5 modulo p is odd. %C A385192 The multiplicative order of 5 modulo a(n) is A385193(n). %C A385192 Contained in primes congruent to 1 or 4 modulo 5 (primes p such that 5 is a quadratic residue modulo p, A045468), and contains primes congruent to 11 or 19 modulo 20 (A122869). %C A385192 Conjecture: this sequence has density 1/3 among the primes. %H A385192 Jianing Song, <a href="/A385192/b385192.txt">Table of n, a(n) for n = 1..10000</a> %e A385192 101 is a term since 5^25 == 1 (mod 101). %t A385192 Select[Prime[Range[200]], OddQ[MultiplicativeOrder[5, #]] &] (* _Paolo Xausa_, Jun 28 2025 *) %o A385192 (PARI) isA385192(p) = isprime(p) && (p!=5) && znorder(Mod(5,p))%2 %Y A385192 Subsequence of A040105, which (without the terms 2 and 5) is itself a subsequence of A045468. %Y A385192 Contains A122869 as a proper subsequence. %Y A385192 Cf. A385193 (the actual multiplicative orders). %Y A385192 Cf. other bases: A014663 (base 2), A385220 (base 3), A385221 (base 4), this sequence (base 5), A163183 (base -2), A385223 (base -3), A385224 (base -4), A385225 (base -5). %K A385192 nonn,easy %O A385192 1,1 %A A385192 _Jianing Song_, Jun 20 2025