A110011 - OEIS

A110011

a(n) = n-F(F(F(F(F(n))))) = n-F^5(n) where F(x)=A120613(x)=floor(phi*floor(x/phi)) and phi=(1+sqrt(5))/2.

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

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OFFSET

1,2

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}.

REFERENCES

Benoit Cloitre, On properties of irrational numbers related to the floor function, in preparation, 2005.

LINKS

Table of n, a(n) for n=1..105.

PROG

(PARI) F(x)=floor((1+sqrt(5))/2*floor((-1+sqrt(5))/2*x)); a(n)=n-F(F(F(F(F(n)))))

CROSSREFS

Cf. A005614 (infinite Fibonacci binary word), A120613.

Cf. sequences for a(n) = n-F^k(n): A003842 (k=1), A110006 (k=2), A110007 (k=3), A110010 (k=4).

Sequence in context: A245353 A063278 A355459 * A138718 A328289 A108922

Adjacent sequences: A110008 A110009 A110010 * A110012 A110013 A110014

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Sep 02 2005

STATUS

approved