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A003571 Order of 3 mod 3n+1.

%I A003571 #19 Oct 22 2023 16:19:28
%S A003571 1,2,6,4,3,4,18,5,20,6,30,16,18,4,42,11,42,6,20,28,10,16,22,12,12,18,
%T A003571 78,8,16,10,6,23,48,20,34,52,27,12,44,29,5,30,126,12,18,16,138,35,28,
%U A003571 18,50,30,78,8,162,41,39,42,60,88,45,22,80,36,16,42,198,100,8
%N A003571 Order of 3 mod 3n+1.
%H A003571 Muniru A Asiru, <a href="/A003571/b003571.txt">Table of n, a(n) for n = 0..5000</a>
%p A003571 a := n -> `if`(n=0, 1, numtheory:-order(3, 3*n+1)):
%p A003571 seq(a(n), n = 0..68);
%t A003571 Table[MultiplicativeOrder[3, 3*n + 1], {n, 0, 68}] (* _Arkadiusz Wesolowski_, Nov 27 2012 *)
%o A003571 (Sage)
%o A003571 def A003571(n):
%o A003571     s, m, N = 0, 1, 3*n + 1
%o A003571     while True:
%o A003571         k = N + m
%o A003571         v = valuation(k, 3)
%o A003571         s += v
%o A003571         m = k // 3^v
%o A003571         if m == 1: break
%o A003571     return s
%o A003571 print([A003571(n) for n in (0..68)]) # _Peter Luschny_, Oct 07 2017
%o A003571 (GAP) List([0..70],n->OrderMod(3,3*n+1)); # _Muniru A Asiru_, Feb 16 2019
%o A003571 (PARI) a(n) = znorder(Mod(3, 3*n+1)); \\ _Michel Marcus_, Feb 16 2019
%Y A003571 Cf. A002326, A003573, A217469.
%K A003571 nonn
%O A003571 0,2
%A A003571 _N. J. A. Sloane_
%E A003571 a(0) = 1 added by _Peter Luschny_, Oct 07 2017