A334223 a(n) is the Y-coordinate of the point at n steps backward from the origin along the space filling curve U defined in A334188; sequence A334222 gives X-coordinates.

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, 6, 7, 8, 8, 8, 9, 10, 10, 9, 8, 8, 8, 8, 9, 10, 11, 11, 10, 9, 9, 10, 11, 12, 12, 12, 13, 14, 15, 15, 14, 13, 13, 14, 15, 15, 14, 13, 12, 11, 11, 12, 13

Offset: 0

Author

Rémy Sigrist, Apr 19 2020

Keywords

• nonn

Examples

			The "backward" branch of curve U starting from the origin is as follows:
     |                                  |
    7|  -15..-16  -21..-22  -31..-32  -37
     |    |    |    |    |    |    |    |
    6|  -14  -17  -20  -23  -30  -33  -36
     |    |    |    |    |    |    |    |
    5|  -13  -18..-19  -24  -29  -34..-35
     |    |              |    |
    4|  -12..-11..-10  -25  -28
     |              |    |    |
    3|   -3...-4   -9  -26..-27
     |    |    |    |
    2|   -2   -5   -8
     |    |    |    |
    1|   -1   -6...-7
     |    |
    0|    0
  ---+-----------------------------------
  y/x|    0    1    2    3    4    5    6
- hence a(10) = a(11) = a(12) = a(25) = a(28) = 4.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8318
• Rémy Sigrist, PARI program for A334223
• Index entries for sequences related to coordinates of 2D curves

Crossrefs

Cf. A334188, A334222.

Programs

PARI

See Links section.

Formula

A334188(a(n), A334223(n)) = -n.