A368148 -id:A368148 - cp's OEIS frontend

A368060 Triangle T(n, k), n > 0, k = 1..n, read and filled in the greedy way by rows such that T(n, k) corresponds to the size of the connected component of terms equal to T(n, k) including the position (n, k).

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

Offset: 1

Rémy Sigrist, Dec 17 2023

This sequence is a variant of A368148.

Empirically, each column is eventually periodic.

			Triangle T(n, k) begins:
              1
             2 2
            1 3 1
           2 2 3 2
          1 3 1 3 2
         2 2 3 2 1 3
        1 3 1 3 2 3 1
       2 2 3 2 1 3 2 2
      1 3 1 3 2 4 1 3 1
     2 2 3 2 1 3 4 2 3 2

Rémy Sigrist, Illustration of initial rows
Rémy Sigrist, Representation of first 500 rows
Rémy Sigrist, PARI program

Cf. A368148.

PARI
```
See Links section.
```

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.

Original entry on oeis.org

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

Rémy Sigrist, Dec 17 2023

nonn

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.

			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

Rémy Sigrist, Illustration of the central part of the spiral
Rémy Sigrist, Representation of the first 500 shells
Rémy Sigrist, PARI program

Cf. A368148.

PARI
```
\\ See Links section.
```

cp's OEIS Frontend

A368060 Triangle T(n, k), n > 0, k = 1..n, read and filled in the greedy way by rows such that T(n, k) corresponds to the size of the connected component of terms equal to T(n, k) including the position (n, k).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI