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A337108
Square spiral constructed by greedy algorithm, so that each diagonal and antidiagonal contains distinct numbers.
1
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).
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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Aug 16 2020
STATUS
approved