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 A385218 #13 Jun 23 2025 10:25:35 %S A385218 30,4290,3710,3150,20090,164430,21114,22490,59514,43494,244650,65110, %T A385218 819930,932190,1011030,1266750,1405410,533830,1864590,135470,2266530, %U A385218 79002,946970,3863190,1039890,4952850,170178,566202,6277530,1324930,3091690,9397290,214314,5054610,3467950,3511090 %N A385218 Multiplicative orders of 2+-i modulo p == 3 (mod 4) that are congruent to 2 modulo 4. %C A385218 Primes p == 3 (mod 4) are precisely the rational primes in the ring of Gaussian integers. %C A385218 Elements in A385165 that are congruent to 2 modulo 4. %C A385218 By definition, a(n) is the multiplicative order of 2+-i modulo A385179(n). %H A385218 Jianing Song, <a href="/A385218/b385218.txt">Table of n, a(n) for n = 1..10000</a> %e A385218 a(7) = 21114 since it is the multiplicative order of 5 modulo A385179(7) = 919, and it is congruent to 2 modulo 4. %o A385218 (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 A385218 forprime(p=3, 1e4, if(p%4==3 && ord(p)%4==2, print1(ord(p), ", "))) %Y A385218 Cf. A385165, A385179 (corresponding primes), A385217, A385219. %K A385218 nonn,easy %O A385218 1,1 %A A385218 _Jianing Song_, Jun 22 2025