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, 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

Offset

0,4

Comments

Is this a shifted version of A036578? - R. J. Mathar, Sep 30 2013 [Yes: see Thm. 4 in Fraenkel (2011). Don Reble, Nov 02 2023]

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-François 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