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

0,7

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).

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

Formula

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A274641 and A308896 for similar sequences.

Cf. A035608.

Sequence in context: A263548 A058496 A137579 * A108805 A283305 A226005

Adjacent sequences: A337105 A337106 A337107 * A337109 A337110 A337111

Keyword

nonn

Author

Rémy Sigrist, Aug 16 2020

Status

approved