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A276857 First differences of the Beatty sequence A022841 for sqrt(7). 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

FORMULA

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

MATHEMATICA

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

Differences[b] (* A276857 *)

CROSSREFS

Cf. A022841, A276873.

Sequence in context: A026240 A124474 A282162 * A244893 A321478 A076982

Adjacent sequences:  A276854 A276855 A276856 * A276858 A276859 A276860

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 24 2016

STATUS

approved

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Last modified March 25 15:02 EDT 2019. Contains 321470 sequences. (Running on oeis4.)