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A144612
Sturmian word of slope (3-sqrt(3))/2.
1
1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1
OFFSET
1,1
COMMENTS
Since 1 - (3-sqrt(3))/2 has a periodic continued fraction expansion with period 21, (a(n)) is the unique fixed point of the morphism 0 -> 10110, 1 -> 101. - Michel Dekking, Feb 05 2017
REFERENCES
J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 286.
LINKS
FORMULA
a(n) = floor((n+1)r) - floor(nr), where r = (3-sqrt(3))/2.
MATHEMATICA
Table[(Floor[(n + 1) (3 - Sqrt[3])/2] - Floor[n (3 - Sqrt[3])/2]), {n, 100}] (* Vincenzo Librandi, Feb 05 2017 *)
PROG
(Magma) [Floor((n+1)*(3-Sqrt(3))/2)-Floor(n*(3-Sqrt(3))/2): n in [1..100]]; // Vincenzo Librandi, Feb 05 2017
CROSSREFS
Cf. A188082.
Sequence in context: A266786 A272532 A166946 * A174208 A141687 A305385
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 13 2009
EXTENSIONS
Corrected and extended by Michel Dekking, Feb 05 2017
STATUS
approved