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Consider trajectory of n under repeated application of map k --> A105108(k); a(n) = length of cycle.
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%I #10 Sep 08 2013 19:54:50

%S 1,1,1,3,3,3,3,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,3,1,9,1,9,3,

%T 1,9,3,1,9,3,1,9,3,1,9,3,1,9,3,1,9,3,1

%N Consider trajectory of n under repeated application of map k --> A105108(k); a(n) = length of cycle.

%C Why is this always a power of 3?

%H David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://neilsloane.com/doc/slopey.pdf">pdf</a>, <a href="http://neilsloane.com/doc/slopey.ps">ps</a>].

%Y Cf. A102370, A105108, A105154.

%K nonn,base

%O 0,4

%A _Philippe Deléham_, Apr 30 2005