A345011 Lexicographically earliest sequence of nonnegative terms forming a clockwise square spiral when nothing else is read except the nonprime/prime nature of the terms (see the Comments section).

0, 2, 3, 1, 5, 4, 7, 6, 8, 11, 9, 10, 13, 12, 14, 15, 17, 16, 18, 20, 19, 21, 22, 24, 25, 23, 26, 27, 28, 30, 29, 32, 33, 34, 35, 36, 31, 38, 39, 40, 42, 44, 37, 45, 46, 48, 49, 50, 51, 41, 52, 54, 55, 56, 57, 58, 43, 60, 62, 63, 64, 65, 66, 68, 47, 69, 70, 72, 74, 75, 76, 77, 53, 78, 80, 81, 82, 84, 85, 86

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..80.

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 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.

Crossrefs

Cf. A345012 (same idea with nonprime/prime digits), A344547 (same idea with even/odd terms), A174344 (an example of a clockwise square spiral).

Sequence in context: A347120 A319068 A335423 * A345012 A345145 A114690

Adjacent sequences: A345008 A345009 A345010 * A345012 A345013 A345014

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Jun 05 2021

Status

approved