A245188 Trajectory of 1 under repeated applications of the morphism 0->12, 1->13, 2->20, 3->21.

1, 3, 2, 1, 2, 0, 1, 3, 2, 0, 1, 2, 1, 3, 2, 1, 2, 0, 1, 2, 1, 3, 2, 0, 1, 3, 2, 1, 2, 0, 1, 3, 2, 0, 1, 2, 1, 3, 2, 0, 1, 3, 2, 1, 2, 0, 1, 2, 1, 3, 2, 1, 2, 0, 1, 3, 2, 0, 1, 2, 1, 3, 2, 1, 2, 0, 1, 2, 1, 3, 2, 0, 1, 3, 2, 1, 2, 0, 1, 2, 1, 3, 2, 1, 2, 0, 1, 3, 2, 0, 1, 2, 1, 3, 2, 0, 1, 3, 2, 1, 2, 0, 1, 3, 2, 0, 1, 2, 1, 3, 2, 1, 2, 0, 1

Offset: 0

Author

N. J. A. Sloane, Jul 21 2014

Keywords

• nonn

Comments

This is the 2-block coding of the Thue-Morse word A010060.

Essentially equal to A005681. - Michel Dekking, Feb 18 2021

Links

• A. Parreau, M. Rigo, E. Rowland, and E. Vandomme, A new approach to the 2-regularity of the l-abelian complexity of 2-automatic sequences, arXiv preprint arXiv:1405.3532 [cs.FL], 2014. See Example 17.
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A010060, A005681.

Programs

Maple

mor := proc(L)
    local Lout,w ;
    if nops(L) = 0 then
        [1,2] ;
    else
        Lout := [] ;
        for w in L do
            if w = 0 then
                Lout := [op(Lout),1,2] ;
            elif w =1 then
                Lout := [op(Lout),1,3] ;
            elif w =2 then
                Lout := [op(Lout),2,0] ;
            else
                Lout := [op(Lout),2,1] ;
            end if;
        end do:
        Lout ;
    end if;
end proc:
L := [1] ;
for r from 0 to 10 do
    Lold := L ;
    L := mor(Lold) ;
    for n from 1 to nops(Lold) do
        if op(n,L) = op(n,Lold) then
            printf("%d,",op(n,L)) ;
        else
            break;
        end if;
    end do:
    print() ;
end do: # R. J. Mathar, Oct 25 2014

Mathematica

(* This gives the first 128 terms. *)
SubstitutionSystem[{0 -> {1, 2}, 1 -> {1, 3}, 2 -> {2, 0}, 3 -> {2, 1}}, {1}, {{7}}] (* Eric Rowland, Oct 02 2016 *)