A274920 Spiral constructed on the nodes of the triangular net in which each new term is the least nonnegative integers distinct from its neighbors.

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

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

Table of n, a(n) for n=0..105.

Formula

a(n) = A274921(n) - 1.

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

Cf. A010872, A080425, A274820, A274821, A274921, A275606, A275610.

Sequence in context: A060024 A143668 A029445 * A316828 A350223 A274820

Adjacent sequences: A274917 A274918 A274919 * A274921 A274922 A274923

Keyword

nonn

Author

Omar E. Pol, Jul 11 2016

Status

approved