

A274920


Spiral constructed on the nodes of the triangular net in which each new term is the least nonnegative integers distinct from its neighbors.


8



0, 1, 2, 1, 2, 1, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 2, 1, 0, 1, 2, 0, 1, 2, 0, 2, 1, 0
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OFFSET

0,3


COMMENTS

The structure of the spiral has the following properties:
1) Positive terms are on the nodes of a hexagonal net.
2) Every 0 is surrounded by three equidistant 1's and three equidistant 2's.
3) Every 1 is surrounded by three equidistant 0's and three equidistant 2's.
4) Every 2 is surrounded by three equidistant 0's and three equidistant 1's.
5) Diagonals are periodic sequences with period 3 (A010872 and A080425).
For the connection with the structure of graphene see also A275606.


LINKS



FORMULA



EXAMPLE

Illustration of initial terms as a spiral:
.
. 2  0  1  2  0  1
. / \
. 0 1  2  0  1  2 0
. / / \ \
. 1 2 0  1  2  0 1 2
. / / / \ \ \
. 2 0 1 2  0  1 2 0 1
. / / / / \ \ \ \
. 0 1 2 0 1  2 0 1 2 0
. / / / / / \ \ \ \ \
. 1 2 0 1 2 0  1 2 0 1 2
. \ \ \ \ \ / / / /
. 0 1 2 0 1  2  0 1 2 0
. \ \ \ \ / / /
. 2 0 1 2  0  1  2 0 1
. \ \ \ / /
. 1 2 0  1  2  0  1 2
. \ \ /
. 0 1  2  0  1  2  0
. \
. 2  0  1  2  0  1
.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



