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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..104.

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 A029368

Adjacent sequences:  A097948 A097949 A097950 * A097952 A097953 A097954

KEYWORD

nonn,uned,obsc

AUTHOR

Roger L. Bagula, Sep 03 2004

STATUS

approved

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Last modified February 24 01:03 EST 2020. Contains 332195 sequences. (Running on oeis4.)