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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
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
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
Sequence in context: A026240 A124474 A282162 * A244893 A321478 A076982
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 24 2016
STATUS
approved