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A003573 Order of 4 mod 4n+1.

%I A003573 #23 Oct 22 2023 16:21:28
%S A003573 1,2,3,6,4,3,10,14,5,18,10,6,21,26,9,30,6,11,9,15,27,4,11,5,24,50,6,
%T A003573 18,14,6,55,50,7,9,34,23,14,74,12,26,33,10,78,86,29,90,18,9,48,98,33,
%U A003573 10,45,35,15,12,30,38,29,39,12,42,41,55,8,42,26,134,6,46,35
%N A003573 Order of 4 mod 4n+1.
%H A003573 Muniru A Asiru, <a href="/A003573/b003573.txt">Table of n, a(n) for n = 0..10000</a>
%F A003573 a(n) = A053447(2*n) for n >= 0. - _Jianing Song_, Oct 03 2022
%p A003573 a := n -> `if`(n=0, 1, numtheory:-order(4, 4*n+1)): seq(a(n), n = 0..68);
%t A003573 Table[MultiplicativeOrder[4, 4*n + 1], {n, 0, 70}] (* _Arkadiusz Wesolowski_, Nov 27 2012 *)
%o A003573 (Sage)
%o A003573 def A003573(n):
%o A003573     s, m, N = 0, 1, 4*n + 1
%o A003573     while True:
%o A003573         k = N + m
%o A003573         v = valuation(k, 4)
%o A003573         s += v
%o A003573         m = k // 4^v
%o A003573         if m == 1: break
%o A003573     return s
%o A003573 print([A003573(n) for n in (0..70)]) # _Peter Luschny_, Oct 07 2017
%o A003573 (GAP) List([0..70],n->OrderMod(4,4*n+1)); # _Muniru A Asiru_, Feb 16 2019
%o A003573 (PARI) a(n) = znorder(Mod(4, 4*n+1)); \\ _Michel Marcus_, Feb 16 2019
%Y A003573 Cf. A003574. First bisection of A053447.
%Y A003573 Cf. A002326, A003571, A217469.
%K A003573 nonn
%O A003573 0,2
%A A003573 _N. J. A. Sloane_
%E A003573 a(0) = 1 added by _Peter Luschny_, Oct 07 2017