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A274820
Spiral constructed on the nodes of the infinite triangular net in which each term is the least nonnegative integer such that no diagonal contains a repeated term.
19
0, 1, 2, 1, 2, 1, 2, 0, 3, 0, 4, 3, 5, 3, 4, 5, 3, 4, 6, 5, 6, 7, 4, 6, 5, 7, 6, 3, 0, 6, 5, 7, 0, 6, 7, 5, 4, 8, 1, 3, 6, 8, 1, 9, 7, 8, 2, 4, 9, 8, 2, 10, 11, 8, 9, 10, 12, 3, 8, 9, 7, 10, 9, 2, 4, 8, 5, 10, 2, 11, 9, 11, 0, 10, 7, 8, 6, 0, 9, 7, 10, 12, 7, 1, 4, 8, 5, 11, 1, 10, 12, 9, 5, 11, 10, 13, 12, 11, 13, 14
OFFSET
0,3
COMMENTS
Also spiral constructed on the infinite hexagonal grid in which each term is the least nonnegative integer such that no diagonal of successive adjacent cells contains a repeated term. Every number is located in the center of a hexagonal cell. Every cell is also the center of three diagonals of successive adjacent cells.
Presumably every line of cells with slope a multiple of 60 degrees (not necessarily passing through the central cell) is a permutation of the nonnegative numbers. See A296343-A296348 for the spokes through the central cell. - N. J. A. Sloane, Dec 12 2017
LINKS
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 illustration of the first 200 windings of the spiral (where the color is a function of a(n))
N. J. A. Sloane, Illustration of initial terms drawn as a spiral on the hexagonal grid (the starting cell is marked in black).
FORMULA
a(n) = A274821(n) - 1.
EXAMPLE
Illustration of initial terms as a spiral:
.
. 9 - 4 - 2 - 8 - 7
. / \
. 8 3 - 6 - 7 - 5 9
. / / \ \
. 2 0 5 - 3 - 4 6 1
. / / / \ \ \
. 10 6 3 1 - 2 0 4 8
. / / / / \ \ \ \
. 11 5 4 2 0 - 1 3 7 6
. \ \ \ \ / / /
. 8 7 5 1 - 2 - 0 6 3
. \ \ \ / /
. 9 0 3 - 4 - 6 - 5 1
. \ \ /
. 10 6 - 7 - 5 - 4 - 8
. \
. 12 - 3 - 8 - 9 - 7
.
PROG
(PARI) See Links section.
CROSSREFS
Cf. A001477, A269526, A274528 (square array), A274641 (spiral on the square grid), A274650 (right triangle), A274821, A274920, A274921, A275606, A275610, A296339.
A296342 says when n first appears.
See A296343-A296348 for the spokes.
Sequence in context: A274920 A316828 A350223 * A230583 A197366 A245715
KEYWORD
nonn,look
AUTHOR
Omar E. Pol, Jul 09 2016
STATUS
approved