cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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).

Original entry on oeis.org

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

Views

Author

Eric Angelini and Carole Dubois, Jun 04 2021

Keywords

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.

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 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).

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).

Original entry on oeis.org

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

Views

Author

Eric Angelini and Carole Dubois, Jun 05 2021

Keywords

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.

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.

Crossrefs

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

A341903 Lexicographically earliest sequence of nonnegative terms forming a clockwise square spiral when nothing else is read except the parity of the digits or the parity of the terms (see the Comments section).

Original entry on oeis.org

0, 1, 3, 2, 5, 4, 7, 6, 8, 9, 20, 10, 201, 22, 210, 24, 21, 26, 28, 12, 20001, 40, 42, 212, 44, 2001, 46, 48, 60, 14, 2000001, 62, 64, 66, 214, 68, 200001, 80, 82, 84, 86, 16, 200000001, 88, 200, 202, 216, 204, 206, 2003, 208, 220, 222, 218, 224, 226, 20003, 228, 240, 242, 2010, 244, 246, 248, 203, 260, 262, 264, 266, 18
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Jun 04 2021

Keywords

Comments

An even term turns the pencil 0 degree to the right, then advances 1 unit; an odd term turns the pencil 90 degrees to the right, then advances 1 unit.
The same spiral is achieved when reading one by one the digits of the sequence (instead of the terms) and using the pencil accordingly.
This is possible as the terms of the sequence were carefully chosen to match the required parities term/digit of the two spirals.

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 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 "digit-only-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.
Similarly, when it comes to a(11) = 20, the "term-only-pencil" reads 20 (even), doesn't change its orientation and advances 1 square. The same term-only-pencil will read later a(12) = 10 (even), won't change its orientation and will advance 1 square again. Those two steps in the same direction match the two steps in the same direction of the "digit-only-pencil). Etc.

Crossrefs

Cf. A344547 (uses only the "term-pencil"), A344548 (uses only the "digit-pencil"), A174344 (an example of a clockwise square spiral).

A345145 Lexicographically earliest sequence of nonnegative terms forming a clockwise square spiral when nothing else is read except the prime/nonprime nature of the terms or the prime/nonprime nature of the digits (see the Comments section).

Original entry on oeis.org

0, 2, 3, 1, 5, 4, 7, 6, 8, 29, 9, 20, 11, 21, 10, 24, 19, 12, 14, 16, 31, 18, 40, 26, 44, 41, 28, 46, 48, 15, 61, 49, 60, 30, 64, 66, 89, 34, 68, 69, 80, 36, 101, 81, 84, 38, 86, 88, 90, 13, 91, 94, 96, 98, 42, 99, 109, 100, 45, 104, 106, 108, 62, 110, 149, 111, 63, 114, 116, 118, 102, 119, 181, 140, 105
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Jun 09 2021

Keywords

Comments

A nonprime term turns the pencil 0 degree to the right, then advances 1 unit; a prime term turns the pencil 90 degrees to the right, then advances 1 unit.
The same spiral is achieved when reading one by one the nonprime/prime digits of the sequence (instead of the terms) and using the pencil accordingly.
This is possible as the terms of the sequence were carefully chosen to place a prime term (respectively, a prime digit) at every corner of the spiral (and nowhere else).

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) = 29, the "term-only-pencil" reads 29 (prime), changes its orientation (by making a right turn) and advances 1 square, then reads a(11) = 9 (nonprime), doesn't change its orientation and advances 1 square;
Similarly, when it comes to a(10) = 29, the "digits-only-pencil" reads the digit 2 (prime), changes its orientation (by making a right turn) and advances 1 square, then reads the digit 9 (nonprime), doesn't change its orientation and advances 1 square;
Those two behaviors of the pencils are equivalent when it comes to draw the clockwise square spiral.

Crossrefs

Cf. A344547, A344548, A174344 (an example of a clockwise square spiral).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.