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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 k-bit number, then so are all numbers in the A105154-orbit of n. For m in the orbit, the i-th bit (i=1,..,k) of A105154(m) is the i-th bit of m-k+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
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
Sequence in context: A238568 A368148 A238421 * A076447 A136690 A144703
KEYWORD
nonn,easy,base
AUTHOR
Philippe Deléham, Apr 30 2005
EXTENSIONS
More terms taken from b-file by Hagen von Eitzen, Jun 24 2009
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)