A144612 Sturmian word of slope (3-sqrt(3))/2.

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

Michel Dekking, Table of n, a(n) for n = 1..2000

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

Adjacent sequences: A144609 A144610 A144611 * A144613 A144614 A144615

Keyword

nonn

Author

N. J. A. Sloane, Jan 13 2009

Extensions

Corrected and extended by Michel Dekking, Feb 05 2017

Status

approved