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

Author

N. J. A. Sloane, Jan 13 2009

Keywords

• nonn

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

Also, sequence of (1 if x is integer, else 0) as x runs over the elements of N U N*sqrt(3) in increasing order, N = {1, 2, 3, ...}. - M. F. Hasler, Feb 06 2025

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

Crossrefs

Cf. A188082, A074065.

Cf. A245222 (= 2 - a(n)),

Programs

Magma

[Floor((n+1)*(3-Sqrt(3))/2)-Floor(n*(3-Sqrt(3))/2): n in [1..100]]; // Vincenzo Librandi, Feb 05 2017

Mathematica

Table[(Floor[(n + 1) (3 - Sqrt[3])/2] - Floor[n (3 - Sqrt[3])/2]), {n, 100}] (* Vincenzo Librandi, Feb 05 2017 *)

Formula

a(n) = floor((n+1)r) - floor(nr), where r = (3-sqrt(3))/2.

a(n) = 2 - A245222(n). - M. F. Hasler, Feb 06 2025

Extensions

Corrected and extended by Michel Dekking, Feb 05 2017