A344547 Lexicographically earliest sequence of nonnegative terms forming a clockwise square spiral when nothing else is read except the parity of the terms (see the Comments section).

0, 1, 3, 2, 5, 4, 7, 6, 8, 9, 10, 12, 11, 14, 16, 18, 13, 20, 22, 24, 15, 26, 28, 30, 32, 17, 34, 36, 38, 40, 19, 42, 44, 46, 48, 50, 21, 52, 54, 56, 58, 60, 23, 62, 64, 66, 68, 70, 72, 25, 74, 76, 78, 80, 82, 84, 27, 86, 88, 90, 92, 94, 96, 98, 29, 100, 102, 104, 106, 108, 110, 112, 31, 114

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..74.

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.

Crossrefs

Cf. A344548 (same idea with digits), A174344 (an example of a clockwise square spiral).

Sequence in context: A297208 A372358 A301941 * A135762 A344548 A341903

Adjacent sequences: A344544 A344545 A344546 * A344548 A344549 A344550

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Jun 04 2021

Status

approved