A263833 Sprague-Grundy sequence G(i-Mark({1,2}, {2})).

0, 1, 2, 0, 1, 2, 3, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 3, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 3, 0, 1, 2, 0, 1, 2

Offset

0,3

Links

Table of n, a(n) for n=0..120.

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

Maple

A263833 := proc(n)
    local strt, q, r, R, Rtz, R1 ;
    strt := [0, 1, 2, 0, 1, 2, 3, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2] ;
    if n <= 17 then
        return op(n+1, strt) ;
    else
        # Theorem 7
        q := floor(n/3) ;
        r := modp(n, 3) ;
        if r = 1 then
            return 0 ;
        elif r =2 then
            return 1;
        else
            # Theorem 8, after correction by E. Sopena
            if type (q, 'even') then
                Rtz := A007814(q) ;
                R1 := q/2^Rtz ;
                if (R1 = 1 or R1 =5) and type(Rtz, 'even') then
                    return 3 ;
                elif R1 <> 1 and R1 <> 5 and type(Rtz, 'odd') then
                    return 3 ;
                else
                    return 2;
                end if;
            else
                return 2;
            end if;
        end if;
    end if;
end proc: # R. J. Mathar, Nov 03 2015

Mathematica

A263833[n_] := Module[{strt, q, r, R, Rtz, R1}, strt = {0, 1, 2, 0, 1, 2, 3, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2}; If[n <= 17, Return[strt[[n+1]]], q = Floor[n/3]; r = Mod[n, 3]; Which[r == 1, Return[0], r == 2, Return[1], True, If[EvenQ[q], Rtz = IntegerExponent[q, 2]; R1 = q/2^Rtz; Which[R1 == 1 || R1 == 5 && EvenQ[Rtz], Return[3], R1 != 1 && R1 != 5 && OddQ[Rtz], Return[3], True, Return[2]], Return[2]]]]];
Table[A263833[n], {n, 0, 120}] (* Jean-François Alcover, Mar 27 2018, after R. J. Mathar *)

Crossrefs

Sequence in context: A323844 A350263 A360677 * A308625 A221469 A350369

Adjacent sequences: A263830 A263831 A263832 * A263834 A263835 A263836

Keyword

nonn

Author

N. J. A. Sloane, Oct 29 2015

Status

approved