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A110007
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a(n)=n-floor(phi*floor(phi^-1*floor(phi*floor(phi^-1*floor(phi*floor(phi^-1*n)))))) where phi=(1+sqrt(5))/2.
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0
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1, 2, 3, 4, 4, 5, 4, 5, 5, 4, 5, 4, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 4, 4, 5, 4, 5, 5, 4, 5, 4, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 4, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 4, 4, 5, 4, 5, 5, 4, 5, 4, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 4, 4, 5, 4, 5, 5, 4, 5, 4, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 4, 4, 5, 4, 5
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OFFSET
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1,2
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COMMENTS
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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 {4,5,4} and each 1 by the block {5,5,4,5,4}. 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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LINKS
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Table of n, a(n) for n=1..105.
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PROG
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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+sqrt(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: A036371 A036370 A005208 * A088527 A030602 A133947
Adjacent sequences: A110004 A110005 A110006 * A110008 A110009 A110010
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre, Sep 02 2005
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STATUS
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approved
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