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A229764 Nim sequence of MARK: the game on n counters in which the legal moves are to remove 1 counter or to halve the number of counters and round down. 0
0, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Is this a shifted version of A036578? - R. J. Mathar, Sep 30 2013

LINKS

Table of n, a(n) for n=0..100.

Aviezri S. Fraenkel, Aperiodic Subtraction Games, The Electronic Journal of Combinatorics, 18(2) (2011).

Eric Sopena, i-Mark: A new subtraction division game, arXiv:1509.04199 [cs.DM], 2015.

MAPLE

a:=proc(n) local i:

option remember:

    if n = 0 then

        return 0:

    else

        for i from 0 while i in {a(n-1), a(floor(n/2))} do od:

    return i:

    fi:

end:

MATHEMATICA

a[0]=0; a[n_] := a[n]=(i=0; While[i==a[n-1] || i==a[Floor[n/2]], i++]; i);

Table[a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Dec 06 2017, from Maple *)

CROSSREFS

Positions of zeros after a(0) given by A036554.

Sequence in context: A139351 A285677 A036578 * A077402 A287418 A125925

Adjacent sequences:  A229761 A229762 A229763 * A229765 A229766 A229767

KEYWORD

nonn

AUTHOR

Nathan Fox, Sep 28 2013

STATUS

approved

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Last modified November 19 14:52 EST 2018. Contains 317352 sequences. (Running on oeis4.)