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A245188 Trajectory of 1 under repeated applications of the morphism 0->12, 1->13, 2->20, 3->21. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

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

LINKS

Table of n, a(n) for n=0..114.

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

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 *)

CROSSREFS

Cf. A010060, A005681.

Sequence in context: A316674 A101479 A136170 * A137241 A331539 A306287

Adjacent sequences:  A245185 A245186 A245187 * A245189 A245190 A245191

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 21 2014

STATUS

approved

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)