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A307285
Coordinates Y_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).
0
0, 3, 6, 10, 15, 20, 23, 27, 30, 33, 39, 44, 47, 50, 53, 56, 59, 62, 65, 70, 73, 76, 79, 82, 85, 88, 91, 94, 99, 102, 105, 110, 113, 116, 119, 122, 125, 130, 133, 136, 139, 142, 147, 150, 153, 158, 161, 164, 169, 172, 175, 178, 181, 184, 189, 192, 195, 198, 201
OFFSET
0,2
COMMENTS
We study Maharaja Nim on the square spiral, as in A307282, A307283, and in particular the P-positions in the 4th quadrant. As in A140100 and A140101 (which are the analogs if we use a Queen instead of a Maharaja) we take the X-axis to point South and the Y-axis to point East.
The P-positions now lie on two roughly straight lines, with coordinates (X_upper(n), Y_upper(n)) with X_upper(n) <= Y_upper(n), and (X_lower(n), Y_lower(n)) with X_lower(n) <= Y_lower(n). These four sequences are A307284-A307287.
The two lines are the hard-to-see black pixels in the fourth quadrant in the Sigrist illustration.
LINKS
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)
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 08 2019
STATUS
approved