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Search: id:A110006
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| A110006 |
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a(n)=n-floor(phi*floor(phi^-1*floor(phi*floor(phi^-1*n)))) where phi=(1+sqrt(5))/2. |
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+0
1
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| 1, 2, 3, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 4, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 4, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 4, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 4, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 4, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 4
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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To built the sequence start from the infinite Fibonacci word : b(n)=floor(n/phi)-floor((n-1)/phi) for n>=1 giving 0,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,..... Then replace each 0 by the block {2,3,3} and each 1 by the block {2,3,3,4,3}. Append an initial 1.
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REFERENCES
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B. Cloitre, On properties of irrational numbers related to the floor function, in preparation, 2005
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PROGRAM
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(PARI) a(n)=n-floor((1+sqrt(5))/2*floor((-1+sqrt(5))/2*floor((1+sqrt(5))/2*floor((-1+sq\ rt(5))/2*n))))
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CROSSREFS
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Cf. A003842 (case a(n)=n-floor(phi*floor(phi^-1*n)), A005614 (infinite Fibonacci binary word).
Sequence in context: A102313 A007538 A025076 this_sequence A137779 A107918 A002963
Adjacent sequences: A110003 A110004 A110005 this_sequence A110007 A110008 A110009
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 02 2005
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