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
Benoit Cloitre, On properties of irrational numbers related to the floor function, in preparation, 2005.
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) F(x)=floor((1+sqrt(5))/2*floor((-1+sqrt(5))/2*x))
a(n)=n-F(F(F(n)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Sep 02 2005
STATUS
approved