login
A307282
Sprague-Grundy values for Maharaja Nim on the counterclockwise square spiral.
7
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)
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.
Sequence in context: A327535 A305902 A245350 * A245354 A097377 A234741
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 05 2019
EXTENSIONS
More terms from Rémy Sigrist, Apr 06 2019
STATUS
approved