A097873 A nonsense sequence

0, 1, 1, 2, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 17, 17, 17, 18, 18, 19, 20, 20, 21, 22, 20, 22, 22, 21, 24, 24, 25, 25, 24, 27, 28, 24, 26, 31, 27, 30, 31, 27, 32, 30, 33, 31, 27, 38

Offset

0,4

Links

Table of n, a(n) for n=0..60.

Formula

A[n_]:=If[(n<33||n>33)&&(n<42||n>45)&&(n<56||n>59), a[[n]].A[n-1], c[[32]].A[n-1]] where A[0] = {{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 4}, {2, 3, 4, 5}};

Mathematica

digits=60
Hofstadter[n_Integer?Positive] :=Hofstadter[n] =Hofstadter[n - Hofstadter[n-1]] + Hofstadter[n - Hofstadter[n-4]] Hofstadter[1] = Hofstadter[2] =1; Hofstadter[3] =2;
Hofstadter[0]= 0; Hofstadter[4]= 3;
n0=4
(* pattern matrices of the chaotic sequence*)
A[k_]=Table[Hofstadter[k+i+j-2], {i, 1, n0}, {j, 1, n0}]
M=Array[f, {n0, n0}]
m1=Flatten[M]
(* linear Markov matrix solutions *)
a=Table[Flatten[M/.Solve[A[n]-M.A[n-1]==0, m1], 1], {n, 1, digits}]; (* function for average matrix calculation*)
ave[n_Integer?Positive] :=ave[n] = (ave[n-1]*(n-1)+a[[n]])/n
ave[1]=a[[1]];
c=Table[ave[n], {n, 1, 32}]; c[[32]]
(* Matrix reconstruction tensors skipping the "bad spots" by substitution of an average matrix*)
B[n_]:=If[(n<33||n>33)&&(n<42||n>45)&&(n<56||n>59), a[[n]].B[n-1], c[[32]].B[n-1]]
B[0] = {{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 4}, {2, 3, 4, 5}};
(* output sequence of the reconstruction*)
b=Flatten[Table[Floor[B[n][[1, 1]]], {n, 0, digits}]]
ListPlot[b, PlotJoined->True, PlotRange->All]

Crossrefs

Sequence in context: A360744 A198454 A063882 * A005375 A138370 A125051

Adjacent sequences: A097870 A097871 A097872 * A097874 A097875 A097876

Keyword

nonn,less,uned

Author

Roger L. Bagula, Sep 01 2004

Status

approved