login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A152270 A switched hidden Markov recursion involving the matrices: Using Alexander Povolotsky three part BBP Pi-digits generator as switching function: f(n)=Floor[Mod[10^k*(7/(4*k + 1) - 6/(4*k + 3) - 1/(4*k + 5)), 3]]; M0 = {{0, 1}, {1, 1/2}}; M = {{0, 2}, {2, 1}}; as Mh=M0.M.(M0+I*f[n]); v[(n)=Mh.v(n-1): first element of v. 1
0, 1, -3, -13, 15, -37, 23, -125, -467, -2269, -2269, -12147, -66877, -66877, -66877, -66877, -370963, -2061725, -11464371, 17899313, 99555423, 99555423, -155471765, -864636987, 1350136841, 1350136841, -2108411107, -2108411107 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The {0,1,2} values of the 3 part Pi-digits behave like a pseudo-random generator but are deterministic in order.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

MATHEMATICA

f[k_] = Floor[Mod[10^k*(7/(4*k + 1) - 6/(4*k + 3) - 1/(4*k + 5)), 3]];

M0 = {{0, 1}, {1, 1/2}}; M = {{0, 2}, {2, 1}};

Mh[n_] := M0.(M.Inverse[f[n]*IdentityMatrix[2] + M0]);

v[0] = {0, 1};

v[n_] := v[n] = Mh[n].v[n - 1]

Table[ -v[n][[1]]/2, {n, 0, 30}]

CROSSREFS

Cf. A006131.

Sequence in context: A032623 A146512 A082704 * A032919 A340018 A216044

Adjacent sequences:  A152267 A152268 A152269 * A152271 A152272 A152273

KEYWORD

sign,uned,obsc,base

AUTHOR

Roger L. Bagula and Alexander R. Povolotsky, Dec 01 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 28 19:33 EDT 2021. Contains 346335 sequences. (Running on oeis4.)