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A110012
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a(n)=n-F(F(n)) where F(x)=floor(sqrt(2)*floor(x/sqrt(2)).
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0
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1, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2
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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 binary word b(k)=floor(k*(sqrt(2)-1))-floor((k-1)*(sqrt(2)-1)) for k>=1 giving 0,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,... Then replace each 0 by the block {2,3,3} and each 1 by the block {2,2,3,3}. Append the initial string {1,2}.
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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) F(x)=floor(sqrt(2)*floor(x/sqrt(2))); a(n)=n-F(F(n))
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CROSSREFS
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Cf. A003842 (case a(n)=n-floor(phi*floor(phi^-1*n)), A006337.
Sequence in context: A055093 A196058 A081844 * A023514 A179751 A039645
Adjacent sequences: A110009 A110010 A110011 * A110013 A110014 A110015
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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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