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%I #11 Jan 30 2017 02:49:38
%S 4,4,4,4,5,4,4,4,5,4,4,4,5,4,4,4,5,4,4,4,4,5,4,4,4,5,4,4,4,5,4,4,4,5,
%T 4,4,4,4,5,4,4,4,5,4,4,4,5,4,4,4,5,4,4,4,4,5,4,4,4,5,4,4,4,5,4,4,4,5,
%U 4,4,4,4,5,4,4,4,5,4,4,4,5,4,4,4,5,4
%N First differences of the Beatty sequence A004976 for 2 + sqrt(5).
%C (a(n+1)) is the unique fixed point of the substitution 4 -> 4445, 5 -> 44454, since alpha = sqrt(5)-2 satisfies 1/(4+alpha) = alpha. See Allouche and Shallit on characteristic words. - _Michel Dekking_, Jan 30 2017
%D J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 285.
%H Clark Kimberling, <a href="/A276866/b276866.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = floor(n*r) - floor(n*r - r), where r = 2 + sqrt(5), n >= 1.
%t z = 500; r = 2+Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}]; (* A004976 *)
%t Differences[b] (* A276866 *)
%Y Cf. A004976, A276884.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Sep 24 2016