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Search: id:A110010
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| A110010 |
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a(n)=n-F(F(F(F(n)))) where F(x)=floor(phi*floor(x/phi)) and phi=(1+sqrt(5))/2. |
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+0
1
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| 1, 2, 3, 4, 5, 6, 6, 7, 6, 6, 7, 6, 5, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 5, 6, 6, 7, 6, 6, 7, 6, 5, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 5, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 5, 6, 6, 7, 6, 6, 7, 6, 5, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 5, 6, 6, 7, 6, 6, 7, 6, 5, 6, 6, 7, 6, 6, 7, 6, 7, 6, 6, 7, 6, 5, 6, 6, 7
(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(k)=floor(k/phi)-floor((k-1)/phi) for k>=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 {5,6,6} and each 1 by the block {7, 6, 6, 7, 6}. Append the initial string {1,2,3,4}.
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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) F(x)=floor((1+sqrt(5))/2*floor((-1+sqrt(5))/2*x)); a(n)=n-F(F(F(F(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: A097623 A069754 A097622 this_sequence A091987 A025544 A121856
Adjacent sequences: A110007 A110008 A110009 this_sequence A110011 A110012 A110013
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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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