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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

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 b-file by Hagen von Eitzen, Jun 24 2009

STATUS

approved

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Last modified May 19 08:25 EDT 2019. Contains 323389 sequences. (Running on oeis4.)