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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.
3
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
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.
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
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Sep 02 2005
STATUS
approved