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A270803 Formal inverse of Thue-Morse sequence A010060. 2
0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0

LINKS

R. J. Mathar, Table of n, a(n) for n = 0..17000

Maciej Gawron, and Maciej Ulas, On formal inverse of the Prouhet-Thue-Morse sequence, Discrete Mathematics 339.5 (2016): 1459-1470. Also arXiv:1601.04840 [math.CO], 2016.

FORMULA

a(0)=0, a(1)=a(2)=1, a(3)=0; thereafter

if n mod 4 = 0 then a(n) = a(n-1),

     if n mod 4 = 1 then a(n) = a(n-2),

     if n mod 4 = 2 then a(n) = a(n-3),

     otherwise a(n) = (a(n-4)+a((n-3)/4)) mod 2.

a(n) = A001002(n)(mod 2), for n > 0. - John M. Campbell, Jul 17 2016

MAPLE

A270803 := proc(n)

    option remember;

    if n <=3 then

        op(n+1, [0, 1, 1, 0]) ;

    else

        if n mod 4 = 0 then

            procname(n-1)

        elif n mod 4 = 1 then

            procname(n-2)

        elif n mod 4 = 2 then

            procname(n-3)

        else

            (procname(n-4)+procname((n-3)/4)) mod 2;

        end if;

    end if;

end proc:

seq(A270803(n), n=0..120) ;

MATHEMATICA

a[n_] := a[n] = Which[n <= 3, {0, 1, 1, 0}[[n + 1]], Mod[n, 4] == 0, a[n - 1], Mod[n, 4] == 1, a[n - 2], Mod[n, 4] == 2, a[n - 3], True, Mod[a[n - 4] + a[(n - 3)/4], 2]];

Table[a[n], {n, 0, 120}] (* Jean-Fran├žois Alcover, Nov 27 2017, from Maple *)

CROSSREFS

Cf. A010060.

See A270804 for positions of 1's

Sequence in context: A095130 A284789 A288736 * A030301 A316341 A284901

Adjacent sequences:  A270800 A270801 A270802 * A270804 A270805 A270806

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 02 2016

STATUS

approved

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Last modified December 15 17:03 EST 2019. Contains 330000 sequences. (Running on oeis4.)