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A089842 Order of each element (row) in A089840, 0 if not finite. 2
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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.
LINKS
CROSSREFS
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].
Sequence in context: A308641 A024676 A093429 * A258569 A091322 A252229
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 05 2003
STATUS
approved

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Last modified March 29 06:34 EDT 2024. Contains 371265 sequences. (Running on oeis4.)