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 A110007 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. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS To build 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}. REFERENCES B. Cloitre, On properties of irrational numbers related to the floor function, in preparation, 2005 LINKS MATHEMATICA Join[{1, 2, 3, 4}, Flatten[Table[Floor[k/GoldenRatio]-Floor[(k-1)/ GoldenRatio], {k, 30}]/.{0->{4, 5, 4}, 1->{5, 5, 4, 5, 4}}]] (* Harvey P. Dale, Dec 12 2017 *) PROG (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)))) CROSSREFS Cf. A003842 (case a(n)=n-floor(phi*floor(phi^-1*n)), A005614 (infinite Fibonacci binary word). Sequence in context: A036371 A036370 A005208 * A327715 A306574 A088527 Adjacent sequences:  A110004 A110005 A110006 * A110008 A110009 A110010 KEYWORD nonn AUTHOR Benoit Cloitre, Sep 02 2005 STATUS approved

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Last modified August 4 21:32 EDT 2021. Contains 346455 sequences. (Running on oeis4.)