A307284 Coordinates X_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

0, 2, 4, 7, 8, 11, 12, 14, 16, 18, 21, 24, 26, 28, 29, 31, 32, 34, 36, 38, 40, 42, 43, 45, 46, 48, 49, 51, 54, 55, 57, 60, 61, 63, 64, 66, 68, 71, 72, 74, 75, 77, 80, 81, 83, 86, 87, 89, 92, 93, 95, 97, 98, 100, 103, 104, 106, 108, 109

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

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.

Sequence in context: A209864 A182654 A112648 * A323108 A187418 A161989

Adjacent sequences: A307281 A307282 A307283 * A307285 A307286 A307287

Keyword

nonn

Author

N. J. A. Sloane, Apr 08 2019

Status

approved