A276857 First differences of the Beatty sequence A022841 for sqrt(7).

2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3

Offset: 1

Author

Clark Kimberling, Sep 24 2016

Keywords

• nonn
• easy

Comments

From Michel Dekking, Mar 09 2019: (Start)

This homogeneous Sturmian sequence, with the first entry removed, is fixed point of the morphism on {2,3} given by

2 -> 32332332332332

3 -> 32332332332332323.

This follows since sqrt(7)-2 has a periodic continued fraction expansion with period [1,1,1,4], see, e.g., Corollary 9.1.6 in Allouche and Shallit. (End)

References

• J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 286.

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A022841, A276873.

Programs

Mathematica

z = 500; r = Sqrt[7]; b = Table[Floor[k*r], {k, 0, z}] (* A022841 *)
Differences[b] (* A276857 *)

Formula

a(n) = floor(n*r) - floor(n*r - r), where r = sqrt(7), n >= 1.