A344548 Lexicographically earliest sequence of nonnegative terms forming a clockwise square spiral when nothing else is read except the parity of the digits (see the Comments section).

0, 1, 3, 2, 5, 4, 7, 6, 8, 9, 20, 10, 22, 12, 24, 14, 26, 21, 28, 40, 16, 42, 44, 18, 46, 48, 30, 60, 62, 23, 64, 66, 68, 32, 80, 82, 84, 34, 86, 88, 201, 200, 202, 203, 204, 206, 205, 208, 220, 222, 36, 224, 226, 207, 228, 240, 242, 25, 244, 246, 248, 27, 260, 262, 264, 209, 266, 268, 280, 221, 282, 284

Offset

1,3

Comments

An even digit turns the pencil 0 degrees to the right, then advances 1 unit; an odd digit turns the pencil 90 degrees to the right, then advances 1 unit.

Links

Table of n, a(n) for n=1..72.

Example

The pencil points towards the East before the start. The 0 doesn't change its orientation and a 1-unit line directed towards the East is traced. As 1 is odd, the pencil turns 90 degrees towards the South and a 1-unit line is traced. As 3 is odd, the pencil turns 90 degrees towards the West and a 1-unit line is traced. As 2 is even, the pencil doesn't change its orientation (towards the West) and a 1-unit line is traced. As 5 is odd, the pencil turns 90 degrees towards the North and a 1-unit line is traced. As 4 is even, the pencil doesn't change its orientation (towards the North) and a 1-unit line is traced. Etc.
When it comes to a(11) = 20, the pencil reads 2 (even), doesn't change its orientation and advances 1 square, then reads 0 (even), doesn't change its orientation and advances 1 square again.
When it comes to a(12) = 10, the pencil reads 1 (odd), turns to the right and advances 1 square, then reads 0 (even), doesn't change its orientation and advances 1 square. Etc.

Crossrefs

Cf. A344547 (same idea with terms), A174344 (an example of a clockwise square spiral).

Sequence in context: A301941 A344547 A135762 * A341903 A066250 A066251

Adjacent sequences: A344545 A344546 A344547 * A344549 A344550 A344551

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Jun 04 2021

Status

approved