A097951 Positive integer values of a chaotic fractional Pisot.

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.

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 A343748

Adjacent sequences: A097948 A097949 A097950 * A097952 A097953 A097954

Keyword

nonn,uned,obsc

Author

Roger L. Bagula, Sep 03 2004

Status

approved