A097873 - OEIS

%I #15 Dec 18 2022 07:03:22

%S 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,

%T 17,17,18,18,19,20,20,21,22,20,22,22,21,24,24,25,25,24,27,28,24,26,31,

%U 27,30,31,27,32,30,33,31,27,38

%N A nonsense sequence

%F 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}};

%t digits=60

%t Hofstadter[n_Integer?Positive] :=Hofstadter[n] =Hofstadter[n - Hofstadter[n-1]] + Hofstadter[n - Hofstadter[n-4]] Hofstadter[1] = Hofstadter[2] =1;Hofstadter[3] =2;

%t Hofstadter[0]= 0; Hofstadter[4]= 3;

%t n0=4

%t (* pattern matrices of the chaotic sequence*)

%t A[k_]=Table[Hofstadter[k+i+j-2], {i, 1, n0}, {j, 1, n0}]

%t M=Array[f, {n0, n0}]

%t m1=Flatten[M]

%t (* linear Markov matrix solutions *)

%t a=Table[Flatten[M/.Solve[A[n]-M.A[n-1]==0, m1], 1], {n, 1, digits}]; (* function for average matrix calculation*)

%t ave[n_Integer?Positive] :=ave[n] = (ave[n-1]*(n-1)+a[[n]])/n

%t ave[1]=a[[1]];

%t c=Table[ave[n], {n, 1, 32}]; c[[32]]

%t (* Matrix reconstruction tensors skipping the "bad spots" by substitution of an average matrix*)

%t 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]]

%t B[0] = {{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 4}, {2, 3, 4, 5}};

%t (* output sequence of the reconstruction*)

%t b=Flatten[Table[Floor[B[n][[1, 1]]], {n, 0, digits}]]

%t ListPlot[b, PlotJoined->True, PlotRange->All]

%K nonn,less,uned

%O 0,4

%A _Roger L. Bagula_, Sep 01 2004