A337108 Square spiral constructed by greedy algorithm, so that each diagonal and antidiagonal contains distinct numbers.

0, 0, 1, 1, 1, 0, 2, 1, 2, 2, 0, 2, 3, 3, 2, 3, 3, 2, 0, 2, 4, 3, 1, 3, 4, 4, 3, 0, 4, 4, 5, 5, 5, 1, 4, 5, 5, 4, 5, 0, 3, 4, 6, 5, 5, 1, 6, 5, 6, 6, 5, 6, 0, 6, 3, 6, 7, 7, 4, 7, 1, 7, 6, 7, 7, 6, 3, 6, 0, 6, 7, 6, 8, 7, 8, 7, 1, 7, 4, 7, 8, 8, 7, 4, 2, 0, 2

Offset: 0

Author

Rémy Sigrist, Aug 16 2020

Keywords

• nonn

Comments

This sequence is a variant of A308896; here we walk a bishop, there a rook.

Visually, we have a superposition of two images that we can separate by considering the parity of the x and y coordinates (see illustrations in Links section).

Examples

			The spiral begins:
        7----7----6----7----1----7----4----7----7
        |                                       |
        6    5----5----4----1----5----5----5    6
        |    |                             |    |
        3    4    3----3----2----3----3    4    3
        |    |    |                   |    |    |
        6    5    2    1----1----1    2    4    6
        |    |    |    |         |    |    |    |
        0    0    0    0    0----0    0    0    0
        |    |    |    |              |    |    |
        6    3    2    2----1----2----2    3    6
        |    |    |                        |    |
        7    4    4----3----1----3----4----4    5
        |    |                                  |
        6    6----5----5----1----6----5----6----6
        |
        8----7----8----7----1----7----4----7----8
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10200
• Rémy Sigrist, Colored representation of the spiral for -512 <= x, y <= 512
• Rémy Sigrist, Colored representation of the spiral for -512 <= x, y <= 512 and x any y have the same parity
• Rémy Sigrist, Colored representation of the spiral for -512 <= x, y <= 512 and x and y have different parity
• Rémy Sigrist, PARI program for A337108

Crossrefs

See A274641 and A308896 for similar sequences.

Cf. A035608.

Programs

PARI

\\ See Links section.

Formula

a(n) = 0 iff n belongs to A035608.