A334221 a(n) is the Y-coordinate of the point at n steps forward from the origin along the space filling curve U defined in A334188; sequence A334220 gives X-coordinates.

0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 1, 2, 3, 3, 2, 1, 1, 2, 3, 4, 4, 4, 5, 6, 6, 5, 4, 4, 4, 3, 2, 1, 1, 2, 3, 3, 2, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 1, 2, 3, 3, 2, 1, 1, 2, 3, 4, 4, 4, 5, 6, 7, 7, 6, 5, 5, 6, 7, 7, 6, 5, 4, 3, 3, 4, 5, 6, 7, 7, 6, 5, 5

Offset: 0

Author

Rémy Sigrist, Apr 19 2020

Keywords

• nonn
• look

Examples

			The "forward" branch of curve U starting from the origin is as follows:
     |
    6|                                      25..
     |                                       |
    5|                                      24
     |                                       |
    4|                            21...22...23
     |                             |
    3|                            20   15...14
     |                             |    |    |
    2|                   5....6   19   16   13
     |                   |    |    |    |    |
    1|                   4    7   18...17   12
     |                   |    |              |
    0|    0....1....2....3    8....9...10...11
  ---+----------------------------------------
  y/x|    0    1    2    3    4    5    6    7
- hence a(5) = a(6) = a(13) = a(16) = a(19) = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8066
• Rémy Sigrist, PARI program for A334221
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A334188, A334220.

Programs

PARI

See Links section.

Formula

A334188(a(n), A334220(n)) = n.