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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 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

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Last modified June 5 16:19 EDT 2020. Contains 334852 sequences. (Running on oeis4.)