%I #11 Mar 09 2019 05:16:36
%S 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,
%T 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,
%U 3,3,2,3,3,2,3,3,2,3,3,2,3,2,3,3,2,3
%N First differences of the Beatty sequence A022841 for sqrt(7).
%C From _Michel Dekking_, Mar 09 2019: (Start)
%C This homogeneous Sturmian sequence, with the first entry removed, is fixed point of the morphism on {2,3} given by
%C 2 -> 32332332332332
%C 3 -> 32332332332332323.
%C 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)
%D J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 286.
%H Clark Kimberling, <a href="/A276857/b276857.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = floor(n*r) - floor(n*r - r), where r = sqrt(7), n >= 1.
%t z = 500; r = Sqrt[7]; b = Table[Floor[k*r], {k, 0, z}] (* A022841 *)
%t Differences[b] (* A276857 *)
%Y Cf. A022841, A276873.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Sep 24 2016