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%I #24 Oct 22 2023 16:56:19
%S 1,1,3,3,2,3,5,7,5,9,5,6,21,13,9,15,3,11,9,15,27,4,11,5,12,25,6,9,7,6,
%T 55,25,7,9,17,23,7,37,12,13,33,10,39,43,29,45,9,9,24,49,33,5,45,35,15,
%U 12,30,19,29,39,6,42,41,55,4,42,13,67,6,23,35,18,34
%N Least number m such that 4^m == +- 1 (mod 4n + 1).
%H Vincenzo Librandi, <a href="/A003560/b003560.txt">Table of n, a(n) for n = 0..5000</a>
%F a(n) <= A003573(n). - _Michel Marcus_, Jun 10 2019
%t Table[Module[{m=1}, While[PowerMod[4, m, 4 n + 1]!=1 && PowerMod[4, m, 4 n + 1]!=4 n, m++]; m], {n, 0, 70}] (* _Vincenzo Librandi_, Jun 10 2019 *)
%o (PARI) a(n) = {my(m=1); while (((mm=Mod(4, 4*n+1)^m) != 1) && (mm != 4*n), m++); m;} \\ _Michel Marcus_, Jun 10 2019
%Y Cf. A003573.
%K nonn
%O 0,3
%A _N. J. A. Sloane_
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