A307282 Sprague-Grundy values for Maharaja Nim on the counterclockwise square spiral.

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

Offset

0,3

Comments

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

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10200 (-50 <= x <= 50 and -50 <= y <= 50)

F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.

Urban Larsson and Johan Wastlund, Maharaja Nim: Wythoff’s Queen meets the Knight, arXiv 1207.0765 [math.CO], 2012.

Urban Larsson and Johan Wästlund, Maharaja Nim: Wythoff's Queen meets the Knight, Integers: Electronic Journal of Combinatorial Number Theory 14 (2014), #G05.

Rémy Sigrist, Colored representation of the spiral for x = -500..500 and y = -500..500 (where the hue is function of T(x,y) and black pixels correspond to 0's)

Rémy Sigrist, PARI program for A307282

N. J. A. Sloane, Illustration of initial terms.

Example

The counterclockwise square spiral begins:
.
  16--15--14--13--12
   |               |
  17   4---3---2  11   .
   |   |       |   |
  18   5   0---1  10   .
   |   |           |
  19   6---7---8---9   .
   |
  20--21--22--23--24--25
.

Prog

(PARI) See Links section.

Crossrefs

For the P-positions see A307283.

Cf. A274641, A308201.

Sequence in context: A327535 A305902 A245350 * A245354 A097377 A234741

Adjacent sequences: A307279 A307280 A307281 * A307283 A307284 A307285

Keyword

nonn

Author

N. J. A. Sloane, Apr 05 2019

Extensions

More terms from Rémy Sigrist, Apr 06 2019

Status

approved