login
Fixed point of the morphism 0 -> 01, 1 -> 012, 2 -> 0; starting with a(1) = 0.
4

%I #17 Mar 20 2023 06:22:36

%S 0,1,0,1,2,0,1,0,1,2,0,0,1,0,1,2,0,1,0,1,2,0,0,1,0,1,0,1,2,0,1,0,1,2,

%T 0,0,1,0,1,2,0,1,0,1,2,0,0,1,0,1,0,1,2,0,1,0,1,2,0,1,0,1,2,0,0,1,0,1,

%U 2,0,1,0,1,2,0,0,1,0,1,0,1,2,0,1,0,1,2,0,0,1,0,1,2

%N Fixed point of the morphism 0 -> 01, 1 -> 012, 2 -> 0; starting with a(1) = 0.

%C After k = 0,1,2,3,... applications of the morphism we have 0, 01, 01012, 01012010120, ... which have lengths 1, 2, 5, 11, 24, 53, 117, ..., satisfying b(n) = 2*b(n-1) + b(n-3) (cf. A052980).

%H N. J. A. Sloane, <a href="/A277731/b277731.txt">Table of n, a(n) for n = 1..20000</a>

%p with(ListTools);

%p T:=proc(S) Flatten(subs( {0=[0,1], 1=[0,1,2], 2=[0]}, S)); end;

%p S:=[0];

%p for n from 1 to 10 do S:=T(S); od:

%p S;

%t m = 100; (* number of terms required *)

%t S[1] = {0};

%t S[n_] := S[n] = SubstitutionSystem[{0 -> {0, 1}, 1 -> {0, 1, 2}, 2 -> {0}}, S[n-1]];

%t For[n = 2, True, n++, If[PadRight[S[n], m] == PadRight[S[n-1], m], Print["n = ", n]; Break[]]];

%t Take[S[n], m] (* _Jean-François Alcover_, Mar 20 2023 *)

%Y Cf. A052980, A277732, A277733, A277734.

%K nonn

%O 1,5

%A _N. J. A. Sloane_, Nov 07 2016