A274641 Counterclockwise square spiral constructed by greedy algorithm, so that each row, column, and diagonal contains distinct numbers. Start with 0 (so in this version a(n) = A274640(n) - 1).

0, 1, 2, 3, 1, 2, 3, 4, 5, 0, 3, 5, 1, 0, 5, 4, 2, 0, 4, 1, 5, 0, 1, 3, 4, 2, 6, 7, 4, 3, 8, 6, 7, 2, 9, 10, 3, 6, 7, 5, 2, 8, 4, 6, 7, 8, 9, 10, 11, 5, 7, 8, 10, 9, 11, 12, 6, 5, 9, 8, 11, 12, 13, 14, 7, 1, 8, 11, 6, 9, 10, 12, 13, 9, 8, 5, 12, 4, 2, 14, 15, 6, 0, 9, 12, 11, 13, 10, 14, 2, 7, 4, 0, 11, 10, 13, 6, 3, 1, 15, 8, 16, 0, 7, 10

Offset

0,3

Comments

See A274640 for further information.

Presumably every row, column, and diagonal is a permutation of the natural numbers, but is there a proof? - N. J. A. Sloane, Jul 10 2016

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..20000 [Based on Alois Heinz's b-file for A274640]

F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.

Rémy Sigrist, Colored representation of the spiral for -500 <= x, y <= 500

N. J. A. Sloane, Confessions of a Sequence Addict (AofA2017), slides of invited talk given at AofA 2017, Jun 19 2017, Princeton. Mentions this sequence.

Example

From Jon E. Schoenfield, Dec 26 2016: (Start)
The spiral begins:
.
   8--15---1---3---6--13--10--11---0---4---7
   |                                       |
  16   7--14--13--12--11---8---9---5---6   2
   |   |                               |   |
   0   1   3--10---9---2---7---6---8  12  14
   |   |   |                       |   |   |
   7   8   6   2---4---5---0---1   3  11  10
   |   |   |   |               |   |   |   |
  10  11   7   0   1---3---2   5   4   9  13
   |   |   |   |   |       |   |   |   |   |
  14   6   5   4   2   0---1   3   7  10  11
   |   |   |   |   |           |   |   |   |
  13   9   2   1   3---4---5---0   6   8  12
   |   |   |   |                   |   |   |
   6  10   8   5---0---1---3---4---2   7   9
   |   |   |                           |   |
   3  12   4---6---7---8---9--10--11---5   0
   |   |                                   |
  11  13---9---8---5--12---4---2--14--15---6
   |
   9--14---0--11--15---7--13--12--10--17--16
.
(End)

Crossrefs

Cf. A274640 (if start with 1 at center), A324481 (position of first n).

For the eight spokes see A324774-A324781.

Sequence in context: A276328 A276332 A359264 * A003315 A194107 A071797

Adjacent sequences: A274638 A274639 A274640 * A274642 A274643 A274644

Keyword

nonn

Author

N. J. A. Sloane, Jul 09 2016, based on the entry A274640 from Zak Seidov and Kerry Mitchell, Jun 30 2016

Status

approved