A345012 Lexicographically earliest sequence of nonnegative terms forming a clockwise square spiral when nothing else is read except the nonprime/prime nature of the digits (see the Comments section).

0, 2, 3, 1, 5, 4, 7, 6, 8, 20, 9, 21, 10, 24, 11, 26, 14, 12, 16, 18, 28, 19, 40, 29, 41, 44, 30, 46, 48, 13, 49, 60, 61, 31, 64, 66, 68, 34, 69, 80, 81, 36, 84, 86, 88, 15, 89, 90, 91, 94, 38, 96, 98, 99, 102, 100, 101, 104, 39, 106, 108, 109, 50, 110, 111, 114, 51, 116, 118, 119, 17, 140, 141, 144, 103

Offset: 1

Author

Eric Angelini and Carole Dubois, Jun 05 2021

Keywords

• base
• nonn

Comments

A nonprime digit turns the pencil 0 degrees to the right, then advances 1 unit; a prime digit turns the pencil 90 degrees to the right, then advances 1 unit.

Examples

			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 2 is prime, the pencil turns 90 degrees towards the South and a 1-unit line is traced. As 3 is prime, the pencil turns 90 degrees towards the West and a 1-unit line is traced. As 1 is nonprime, the pencil doesn't change its orientation (towards the West) and a 1-unit line is traced. As 5 is prime, the pencil turns 90 degrees towards the North and a 1-unit line is traced. As 4 is nonprime, the pencil doesn't change its orientation (towards the North) and a 1-unit line is traced. Etc.
When it comes to a(10) = 20, the pencil reads 2 (prime), turns to the right and advances 1 square, then reads 0 (nonprime), doesn't change its orientation and advances 1 square again. Etc.
		

Crossrefs

Cf. A345011 (same idea with nonprime/prime terms), A344548 (same idea with even/odd digits), A174344 (an example of a clockwise square spiral).