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%I #9 Nov 09 2018 22:21:21
%S 1,2,2,0,1,2,1,1,2,0,0,1,1,2,3,1,0,0,1,2,3,0,1,2,0,0,0,0,1,1,1,1,2,1,
%T 1,1,1,1,2,1,2,3,1,1,1,1,2,3,0,1,1,1,1,2,0,1,1,1,2,3,0,0,0,1,2,3,0,1,
%U 2,0,0,0,0,1,2,1,1,2,1,1,2,1,1,2,1,2,3,1,1,1,1,2,3,0,1,2,1,1,2,0,1,2,1,2,4
%N Positive integer values of a chaotic fractional Pisot.
%C The manifold is developed from a fractional power eigenvalue matrix Bezier with determinant adjusted to one and a minimal value of b found by examination.
%F M=N[{{0.1, 0}, {1/2, (b + sqrt(x))/6, 1/2, {1, b, -1}}; A[n_]:=M.A[n-1]; A[0]:={{0, 1, 1}, {1, 1, 2}, {1, 2, 2}}.
%t (* Fractional Pisot 3 X 3 Markov sequence *)
%t Clear[M, A, x]; digits = 21; b = -5/4; x = (n + 1)/n;
%t M = N[{{0.1, 0}, {1/2, (b + Sqrt[x])/6, 1/2, {1, b, -1}};
%t A[n_] := M.A[n - 1]; A[0] := {{0, 1, 1}, {1, 1, 2}, {1, 2, 2}};
%t (* flattened sequence of 3 X 3 matrices made with a Fractional Pisot recurrence *)
%t b = Flatten[Table[M.A[n], {n, 1, digits}]]; Floor[Abs[b]]
%K nonn,uned,obsc
%O 0,2
%A _Roger L. Bagula_, Sep 03 2004
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