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A110011
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a(n)=n-F(F(F(F(F(n)))))=n-F^5(n) where F(x)=floor(phi*floor(x/phi)) and phi=(1+sqrt(5))/2.
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0
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1, 2, 3, 4, 5, 6, 7, 8, 8, 7, 8, 8, 7, 8, 7, 8, 8, 7, 8, 8, 9, 8, 7, 8, 8, 7, 8, 7, 8, 8, 7, 8, 8, 7, 8, 7, 8, 8, 7, 8, 8, 9, 8, 7, 8, 8, 7, 8, 7, 8, 8, 7, 8, 8, 9, 8, 7, 8, 8, 7, 8, 7, 8, 8, 7, 8, 8, 7, 8, 7, 8, 8, 7, 8, 8, 9, 8, 7, 8, 8, 7, 8, 7, 8, 8, 7, 8, 8, 7, 8, 7, 8, 8, 7, 8, 8, 9, 8, 7, 8, 8, 7, 8, 7, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| To built the sequence start from the infinite Fibonacci word b(k)=floor(k/phi)-floor((k-1)/phi) for k>=2 giving 1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,..... Then replace each 0 by the block {9,8,7,8,8,7,8,7,8,8,7,8,8} and each 1 by the block {9,8,7,8,8,7,8,7,8,8,7,8,8,7,8,7,8,8,7,8,8}. Append the initial string {1,2,3,4,5,6,7,8,8,7,8,8,7,8,7,8,8,7,8,8}.
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REFERENCES
| B. Cloitre, On properties of irrational numbers related to the floor function, in preparation, 2005
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PROG
| (PARI) F(x)=floor((1+sqrt(5))/2*floor((-1+sqrt(5))/2*x)); a(n)=n-F(F(F(F(F(n)))))
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CROSSREFS
| Cf. A003842 (case a(n)=n-floor(phi*floor(phi^-1*n)), A005614 (infinite Fibonacci binary word).
Sequence in context: A017893 A017883 A063278 * A138718 A108922 A102670
Adjacent sequences: A110008 A110009 A110010 * A110012 A110013 A110014
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 02 2005
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