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 A385217 #11 Jun 23 2025 10:24:43 %S A385217 13695,40755,7475,19895,43995,117855,138075,13185,69445,87725,308505, %T A385217 220665,567645,80735,1103355,1321125,1386945,507795,1594005,130995, %U A385217 205975,2051325,2092035,2216565,2703975,1368315,2750685,504095,3039345,212605,3342405,125081,1274665,3991725,152205,4279275 %N A385217 Odd multiplicative orders of 2+-i modulo primes p == 3 (mod 4). %C A385217 Primes p == 3 (mod 4) are precisely the rational primes in the ring of Gaussian integers. %C A385217 Odd elements in A385165. %C A385217 By definition, a(n) is the multiplicative order of 2+-i modulo A385169(n). %H A385217 Jianing Song, <a href="/A385217/b385217.txt">Table of n, a(n) for n = 1..10000</a> %e A385217 a(49) = 635253 since it is the multiplicative order of 5 modulo A385169(49) = 8731, and it is odd. %e A385217 a(50) = 57447 since it is the multiplicative order of 5 modulo A385169(50) = 8839, and it is odd. %e A385217 a(51) = 2029953 since it is the multiplicative order of 5 modulo A385169(51) = 9011, and it is odd. %o A385217 (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 A385217 forprime(p=3, 1e4, if(p%4==3 && ord(p)%2, print1(ord(p), ", "))) %Y A385217 Cf. A385165, A385169 (corresponding primes), A385218, A385219. %K A385217 nonn,easy %O A385217 1,1 %A A385217 _Jianing Song_, Jun 22 2025