A105154 Consider trajectory of n under repeated application of map k -> A105027(k); a(n) = length of cycle.

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

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: A238568 A368148 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