cp's OEIS Frontend

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.

A385219 Multiplicative orders of 2+-i modulo p == 3 (mod 4) that are not divisible by 2 or 3.

This page as a plain text file.
%I A385219 #13 Jun 23 2025 10:25:31
%S A385219 7475,19895,69445,87725,80735,205975,504095,212605,125081,1274665,
%T A385219 720055,181445,1044005,492929,891335,1346365,5501795,7360445,8179505,
%U A385219 9489095,10628035,3850775,3138905,14618765,15377605,34181,17907265,21377825,23942035,5047511,13694965,6868865,28713125
%N A385219 Multiplicative orders of 2+-i modulo p == 3 (mod 4) that are not divisible by 2 or 3.
%C A385219 Primes p == 3 (mod 4) are precisely the rational primes in the ring of Gaussian integers.
%C A385219 Elements in A385165 that are not divisible by 2 or 3.
%C A385219 By definition, a(n) is the multiplicative order of 2+-i modulo A385188(n).
%H A385219 Jianing Song, <a href="/A385219/b385219.txt">Table of n, a(n) for n = 1..10000</a>
%F A385219 a(9) = 125081 since it is the multiplicative order of 5 modulo A385188(9) = 5479, and it is divisible by neither 2 nor 3.
%o A385219 (PARI) ord(p) = my(d = divisors((p+1)*znorder(Mod(5, p)))); for(i=1, #d, if(Mod([2, -1; 1, 2], p)^d[i] == 1, return(d[i]))) \\ for a prime p == 3 (mod 4), returns ord(2+-i, p)
%o A385219 forprime(p=3, 1e4, if(p%4==3 && ord(p)%2 && ord(p)%3, print1(ord(p), ", ")))
%Y A385219 Cf. A385165, A385188 (corresponding primes), A385217, A385218.
%K A385219 nonn,easy
%O A385219 1,1
%A A385219 _Jianing Song_, Jun 22 2025