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
Rémy Sigrist, Table of n, a(n) for n = 0..120400
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, PARI program for A274820
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
KEYWORD
nonn,look
AUTHOR
Omar E. Pol, Jul 09 2016
STATUS
approved