A334223 a(n) is the Y-coordinate of the point at n steps backward from the origine 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

0,3

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

Formula

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

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A334188, A334222.

Sequence in context: A131838 A274885 A287732 * A171414 A270921 A038529

Adjacent sequences: A334220 A334221 A334222 * A334224 A334225 A334226

Keyword

nonn

Author

Rémy Sigrist, Apr 19 2020

Status

approved