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A097951
Positive integer values of a chaotic fractional Pisot.
0
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, 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, 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
OFFSET
0,2
COMMENTS
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.
FORMULA
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}}.
MATHEMATICA
(* Fractional Pisot 3 X 3 Markov sequence *)
Clear[M, A, x]; digits = 21; b = -5/4; x = (n + 1)/n;
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}};
(* flattened sequence of 3 X 3 matrices made with a Fractional Pisot recurrence *)
b = Flatten[Table[M.A[n], {n, 1, digits}]]; Floor[Abs[b]]
CROSSREFS
Sequence in context: A091269 A287455 A216789 * A256171 A058643 A343748
KEYWORD
nonn,uned,obsc
AUTHOR
Roger L. Bagula, Sep 03 2004
STATUS
approved