

A105154


Consider trajectory of n under repeated application of map k > A105027(k); a(n) = length of cycle.


4



1, 1, 2, 2, 2, 1, 2, 1, 4, 2, 2, 4, 4, 2, 2, 4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 4, 1, 4, 8, 4, 4, 4, 4, 8, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 16, 8, 4, 2, 4, 8, 16, 2, 16, 8, 4, 2, 4, 8, 16, 2, 16, 8, 4, 2, 4, 8, 16, 2, 16, 8, 4, 2, 4, 8, 16, 2, 16, 8, 4, 2, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

Why is this always a power of 2?
a(n) is always a power of 2: If n is a kbit number, then so are all numbers in the A105154orbit of n. For m in the orbit, the ith bit (i=1,..,k) of A105154(m) is the ith bit of mk+i and hence depends only on the lower i bits of m. By induction quickly follows that the lower i bits run through a cycle of length dividing 2^i. This also shows that a(n) <= n for n > 0.


LINKS

Hagen von Eitzen, Table of n, a(n) for n = 0..10000
David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].


PROG

(Haskell)
a105154 n = t [n] where
t xs@(x:_)  y `elem` xs = length xs
 otherwise = t (y : xs) where y = a105027 x
 Reinhard Zumkeller, Jul 21 2012


CROSSREFS

Cf. A102370, A105025, A105027, A105153.
Sequence in context: A237523 A238568 A238421 * A076447 A136690 A144703
Adjacent sequences: A105151 A105152 A105153 * A105155 A105156 A105157


KEYWORD

nonn,easy,base


AUTHOR

Philippe Deléham, Apr 30 2005


EXTENSIONS

More terms taken from bfile by Hagen von Eitzen, Jun 24 2009


STATUS

approved



