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A161593 Lengths of new periods in the RATS sequence (0 replacing infinity).

%I A161593 #18 Dec 31 2022 10:45:42
%S A161593 0,8,2,18,2,2,2,14,2,3,2,2,2,6
%N A161593 Lengths of new periods in the RATS sequence (0 replacing infinity).
%C A161593 The values A114611(j) for those starting values j of the RATS mapping x->A036839(x) which end in cycles that cannot be reached starting from any smaller j.
%C A161593 Every integer > 1 appears in this sequence. - _Andrey Zabolotskiy_, Jun 11 2017
%C A161593 For other terms see Branicky link. - _Michael S. Branicky_, Dec 30 2022
%H A161593 Michael S. Branicky, <a href="/A161596/a161596_1.txt">RATS Sequence Cycles</a>.
%H A161593 Curtis Cooper, <a href="http://cs.ucmo.edu/~cnc8851/rats.html">RATS</a>.
%H A161593 Curtis Cooper and Robert E. Kennedy, <a href="https://doi.org/10.1007/978-94-011-4271-7_9">Base 10 RATS Cycles and Arbitrarily Long Base 10 RATS Cycles</a>, Applications of Fibonacci numbers, Vol. 8, Kluwer Acad. Publ., Dordrecht, 1999, pages 83-93.
%H A161593 Tanya Khovanova, <a href="http://blog.tanyakhovanova.com/?p=155">Destinies of Numbers</a>.
%e A161593 a(1)=A114611(0). a(2)=A114611(j=3)=8 with a cycle of length 8 shown in A066710.
%e A161593 A114611(j=6)=8 does not contribute because the cycle is the same as reached from j=3.
%e A161593 a(3)=A114611(9)=2 with a new cycle of length 2 shown in A066711.
%e A161593 A114611(j=12)=8 does not contribute because the cycle is the same as reached from j=3.
%e A161593 A114611(j=15)=8 does not contribute because 15->66->123 is the cycle as reached from j=3.
%e A161593 A114611(j=18)=2 does not contribute because the cycle is the same as reached from j=9.
%e A161593 A114611(j=21)=8 does not contribute because 21->33->66 reaches the same cycle as started from j=3.
%e A161593 a(4)=A114611(j=29)=18.
%Y A161593 Cf. A004000, A036839, A066711, A066710, A288537.
%Y A161593 Cf. A161590, A161592, A161596.
%K A161593 more,nonn,base
%O A161593 1,2
%A A161593 _J. H. Conway_ and _Tanya Khovanova_, Jun 14 2009
%E A161593 Comment and examples added by _R. J. Mathar_, Jul 07 2009
%E A161593 a(9)-a(14) from _Michael S. Branicky_, Dec 30 2022