%I #9 Mar 31 2012 14:02:29
%S 1,2,2,2,3,2,3,2,2,3,2,3,0,0,0,4,0,0,0,0,0,4,2,2,3,2,3,2,2,3,4,3,4,2,
%T 3,3,4,2,4,2,3,2,4,3,4,2,2,3,2,3,2,2,3,4,3,4,2,3,3,4,2,4,2,3,2,4,3,4,
%U 2,2,3,2,3,2,2,3,4,3,4,2,3,3,4,2,4,2,3,2,4,3,4,2,2,3,2,3,2,2,3,4,3,4
%N Order of each element (row) in A089840, 0 if not finite.
%C If a(n) is nonzero, then the n-th non-recursive Catalan Automorphism in A089840 does not have orbits (cycles) larger than that and the corresponding LCM-sequence will set to a constant sequence a(n),a(n),a(n),a(n),... E.g. A089840[4] = A089851 is obtained by rotating three subtrees cyclically and its LCM-sequence begins as 1,1,1,3,3,3,3,3,3,3,3,... (a(4)=3). Similarly, A089840[15] = A089859, whose LCM-sequence begins as 1,1,2,4,4,4,4,4,4,4,4,.... (a(15)=4). In contrast, the Max. cycle and LCM-sequence (A089410) of A089840[12] (= A074679) exhibits genuine growth, thus a(12)=0.
%H A. Karttunen, <a href="/A089839/a089839.c.txt">C-program for computing the initial terms of this sequence</a>
%Y Note that the terms 1-23 of A060131: 2, 2, 3, 2, 3, 2, 2, 3, 4, 3, 4, 2, 3, 3, 4, 2, 4, 2, 3, 2, 4, 3, 4 repeat here at positions [22..44], [45..67], [68..90], [91..113], [114..136].
%K nonn
%O 0,2
%A _Antti Karttunen_, Dec 05 2003