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A105153
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Consider trajectory of n under repeated application of map k -> A105025(k); a(n) = length of cycle.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Why is this always a power of 2?
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LINKS
| David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
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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 (mathar(AT)strw.leidenuniv.nl), Aug 10 2007
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CROSSREFS
| Positions of 1's: A105271.
Cf. A102370, A105025, A105027, A105154.
Sequence in context: A061498 A106029 A188431 * A000924 A187201 A109909
Adjacent sequences: A105150 A105151 A105152 * A105154 A105155 A105156
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KEYWORD
| nonn,easy,base
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 30 2005
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 10 2007
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