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

Author

N. J. A. Sloane, Apr 05 2019

Keywords

• nonn

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.

Examples

			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
.
		

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.

Crossrefs

For the P-positions see A307283.

Cf. A274641, A308201.

Programs

PARI

See Links section.

Extensions

More terms from Rémy Sigrist, Apr 06 2019