A171949 P-positions for game of Mark-4.

0, 4, 8, 12, 20, 24, 28, 36, 40, 44, 52, 56, 60, 64, 68, 72, 76, 84, 88, 92, 100, 104, 108, 116, 120, 124, 128, 132, 136, 140, 148, 152, 156, 164, 168, 172, 180, 184, 188, 192, 196, 200, 204, 212, 216, 220, 228, 232, 236, 244, 248, 252, 260, 264, 268, 276

Offset: 1

Author

N. J. A. Sloane, Oct 29 2010

Keywords

• nonn
• easy

Links

• Aviezri S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math. 312 (1) (2012) 42-46.

Crossrefs

Complement of A171948.

Cf. A217319.

Programs

Maple

isA171948 := proc(n)
    option remember;
    if n <=3 then
        true;
    elif isA171949(n) then
        false;
    else
        true ;
    end if;
end proc:
isA171949 := proc(n)
    option remember;
    if n mod 4 <> 0 then
        return false;
    end if;
    if isA171948(n/4) then
        true;
    else
        false ;
    end if;
end proc:
for n from 0 to 400 do
    if isA171949(n) then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Mar 28 2013

Mathematica

isA171948[n_] := isA171948[n] =
   If[n <= 3, True, If[isA171949[n], False, True]];
isA171949[n_] := isA171949[n] =
   If[Mod[n, 4] != 0, False, If[isA171948[n/4], True, False]];
Select[Range[0, 400], isA171949] (* Jean-François Alcover, Apr 16 2023, after R. J. Mathar *)

Formula

a(n) = 4*A171948(n).

Conjecture: For n>=2, a(n) = A217319(n-1). - Vladimir Shevelev, Mar 18 2013