A368212 Square spiral of positive integers built by greedy algorithm such that each value corresponds to the area of the connected component with terms of the same value and containing this value.

1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 3, 1, 3, 2, 3, 1, 3, 2, 3, 1, 3, 2, 3, 1, 2, 3, 1, 3, 2, 1, 2, 3, 1, 3, 2, 1, 2, 3, 1, 3, 2, 1, 2, 3, 1, 3, 2, 1, 3, 2, 3, 2, 3, 2, 3, 1, 3, 2, 3, 2, 3, 2, 3, 1, 3, 2, 3, 2, 3, 2, 3, 1, 3, 2, 3, 2, 3, 2, 3, 1, 2, 3, 1, 4, 2, 1

Offset

0,2

Comments

In other words, we tile the plane with polyominoes as small as possible, and for any k > 0, two k-ominoes cannot share an edge.

This sequence is a variant of A368148.

Empirically, the spiral has 4-fold rotational symmetry.

Links

Table of n, a(n) for n=0..86.

Rémy Sigrist, Illustration of the central part of the spiral

Rémy Sigrist, Representation of the first 500 shells

Rémy Sigrist, PARI program

Example

The spiral begins:
        1---3---2---3---1
        |               |
        3   1---2---1   3
        |   |       |   |
        2   2   1---2   2
        |   |           |
        3   1---2---1---3
        |
        1---3---2---3---1

Prog

(PARI) See Links section.

Crossrefs

Cf. A368148.

Sequence in context: A309025 A247599 A083897 * A025823 A025821 A161233

Adjacent sequences: A368209 A368210 A368211 * A368213 A368214 A368215

Keyword

nonn

Author

Rémy Sigrist, Dec 17 2023

Status

approved