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 A385163 #16 Jun 20 2025 12:42:32
%S A385163 8,24,40,72,88,40,56,184,232,264,280,312,328,408,424,56,520,552,120,
%T A385163 648,664,712,760,792,840,296,904,952,200,1048,1080,376,408,1240,120,
%U A385163 1384,1432,1464,1512,1528,1672,344,584,1768,1848,1864,1912,1944,1960,664,2008,2088,2184,2248,456
%N A385163 Let p = A002145(n) be the n-th prime == 3 (mod 4); a(n) is the multiplicative order of 1+-i modulo p in Gaussian integers.
%C A385163 Also, a(n) is the multiplicative order of the matrix [1,-1;1,1] or [1,1;-1,1] modulo p.
%C A385163 Note that (1+-i)^4 = -4. Since (1+-i)^n is a real number if and only if n is divisible by 4, we have a(n) = 4*ord(-4,p), where ord(a,p) is the multiplicative order of a modulo p.
%H A385163 Jianing Song, <a href="/A385163/b385163.txt">Table of n, a(n) for n = 1..10000</a>
%e A385163 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.
%o A385163 (PARI) forprime(p=3, 1e3, if(p%4==3, print1(4*znorder(Mod(-4,p)), ", ")))
%Y A385163 Cf. A002145, A384164 ({a(n)/8}), A385165 (multiplicative order of 2+-i).
%K A385163 nonn,easy
%O A385163 1,1
%A A385163 _Jianing Song_, Jun 20 2025