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Sprague-Grundy values for Maharaja Nim on the counterclockwise square spiral.
7

%I #34 Mar 07 2020 13:52:25

%S 0,1,2,3,4,5,6,7,8,4,6,5,7,9,8,10,1,9,2,10,3,9,11,10,2,0,3,11,10,4,1,

%T 0,6,12,7,5,3,0,8,7,1,4,5,0,2,1,12,13,6,7,1,14,8,12,3,2,9,8,10,3,2,13,

%U 4,6,7,11,13,6,12,15,14,16,8,10,7,14,4,5,3,15

%N Sprague-Grundy values for Maharaja Nim on the counterclockwise square spiral.

%C A Maharaja is a piece which can move both like a queen and a knight.

%C A274641 is the analogous sequence if the piece is a chess queen.

%H Rémy Sigrist, <a href="/A307282/b307282.txt">Table of n, a(n) for n = 0..10200</a> (-50 <= x <= 50 and -50 <= y <= 50)

%H F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, <a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i1p52/8039">Queens in exile: non-attacking queens on infinite chess boards</a>, Electronic J. Combin., 27:1 (2020), #P1.52.

%H Urban Larsson and Johan Wastlund, <a href="https://arxiv.org/abs/1207.0765">Maharaja Nim: Wythoff’s Queen meets the Knight</a>, arXiv 1207.0765 [math.CO], 2012.

%H Urban Larsson and Johan Wästlund, <a href="https://www.emis.de/journals/INTEGERS/papers/og5/og5.Abstract.html">Maharaja Nim: Wythoff's Queen meets the Knight</a>, Integers: Electronic Journal of Combinatorial Number Theory 14 (2014), #G05.

%H Rémy Sigrist, <a href="/A307282/a307282_1.png">Colored representation of the spiral for x = -500..500 and y = -500..500</a> (where the hue is function of T(x,y) and black pixels correspond to 0's)

%H Rémy Sigrist, <a href="/A307282/a307282.gp.txt">PARI program for A307282</a>

%H N. J. A. Sloane, <a href="/A307282/a307282.png">Illustration of initial terms.</a>

%e The counterclockwise square spiral begins:

%e .

%e 16--15--14--13--12

%e | |

%e 17 4---3---2 11 .

%e | | | |

%e 18 5 0---1 10 .

%e | | |

%e 19 6---7---8---9 .

%e |

%e 20--21--22--23--24--25

%e .

%o (PARI) See Links section.

%Y For the P-positions see A307283.

%Y Cf. A274641, A308201.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Apr 05 2019

%E More terms from _Rémy Sigrist_, Apr 06 2019