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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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2
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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
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OFFSET
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0,3
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COMMENTS
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Why is this always a power of 2?
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LINKS
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David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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