A307287 Coordinates Y_lower(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

0, 1, 9, 13, 19, 22, 37, 52, 58, 69, 78, 84, 90, 101, 112, 118, 132, 138, 149, 160, 171, 180, 191, 200, 211, 222, 228, 237, 248, 259, 268, 279, 288, 299, 308, 319, 325, 336, 345, 356, 362, 373, 382, 393, 402, 413, 424, 430, 441, 450, 461, 470, 481, 487, 498

Offset: 0

Author

N. J. A. Sloane, Apr 08 2019

Keywords

• nonn

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, Table of n, a(n) for n = 0..58
• 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)

Crossrefs

Cf. A140100, A140101, A307282, A307283, A307284-A307287.

Extensions

More terms from Rémy Sigrist, Apr 09 2019