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 A110012 a(n)=n-F(F(n)) where F(x)=floor(sqrt(2)*floor(x/sqrt(2)). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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}. REFERENCES B. Cloitre, On properties of irrational numbers related to the floor function, in preparation, 2005 LINKS PROG (PARI) F(x)=floor(sqrt(2)*floor(x/sqrt(2))); a(n)=n-F(F(n)) CROSSREFS 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 KEYWORD nonn AUTHOR Benoit Cloitre, Sep 02 2005 STATUS approved

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