

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
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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



