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 A385164 #14 Jun 20 2025 15:07:38 %S A385164 1,3,5,9,11,5,7,23,29,33,35,39,41,51,53,7,65,69,15,81,83,89,95,99,105, %T A385164 37,113,119,25,131,135,47,51,155,15,173,179,183,189,191,209,43,73,221, %U A385164 231,233,239,243,245,83,251,261,273,281,57,293,299,303,309,45,107,323,329,11,115 %N A385164 Let p = A002145(n) be the n-th prime == 3 (mod 4); 8*a(n) is the multiplicative order of 1+-i modulo p in Gaussian integers. %H A385164 Jianing Song, <a href="/A385164/b385164.txt">Table of n, a(n) for n = 1..10000</a> %F A385164 a(n) = ord(-4,p)/2, where ord(a,p) is the multiplicative order of a modulo p. %e A385164 For A002145(4) = 19: Since (1+i)^(4k) = (-4)^k, we have (1+i)^72 == 1 (mod 19), and 72 is the smallest such exponent. Hence a(4) = 72/8 = 9. %o A385164 (PARI) forprime(p=3, 1e3, if(p%4==3, print1(znorder(Mod(-4,p))/2, ", "))) %Y A385164 Cf. A002145, A385163. %K A385164 nonn,easy %O A385164 1,2 %A A385164 _Jianing Song_, Jun 20 2025