A105153 Consider trajectory of n under repeated application of map k -> A105025(k); a(n) = length of cycle.

1, 1, 2, 2, 1, 2, 1, 2, 4, 2, 2, 4, 4, 2, 2, 4, 4, 1, 4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 4, 1, 4, 4, 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, 8, 4, 4, 4, 4, 8, 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, 8, 16, 2, 16, 8, 4, 2

Offset

0,3

Comments

Why is this always a power of 2?

Links

Reinhard Zumkeller, 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

(C++) #include <iostream> #include <vector> #include <set> using namespace std ; int main(int argc, char *argv[]) { int kmax = 8 ; vector<int> a105025; a105025.push_back(0) ; a105025.push_back(1) ; for(int k=1 ; k < kmax ; k++) { int bstrt = 1 << k ; for(int j=0 ; j < bstrt ; j++) { int s = bstrt ; for(int i= k-1 ; i >=0 ; i--) s += (bstrt+j+k-i) & ( 1<<i) ; a105025.push_back(s) ; /* cout << s << endl ; */ } } for(int n=0; n < a105025.size() ; n++) { int nrep = n ; set<int> traj ; while ( traj.find(nrep) == traj.end() ) { traj.insert(nrep) ; if ( nrep < a105025.size() ) nrep = a105025[nrep] ; else break ; } cout << traj.size() << ", " ; } cout << endl ; return 0 ; } - R. J. Mathar, Aug 10 2007
(Haskell)
a105153 n = t [n] where
   t xs@(x:_) | y `elem` xs = length xs
              | otherwise   = t (y : xs) where y = a105025 x
-- Reinhard Zumkeller, Jul 21 2012

Crossrefs

Positions of 1's: A105271.

Cf. A102370, A105025, A105027, A105154.

Sequence in context: A106029 A260311 A188431 * A000924 A306911 A348406

Adjacent sequences: A105150 A105151 A105152 * A105154 A105155 A105156

Keyword

nonn,easy,base

Author

Philippe Deléham, Apr 30 2005

Extensions

More terms from R. J. Mathar, Aug 10 2007

Status

approved