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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.)