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 1-5 of 5 results.

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

Original entry on oeis.org

0, 1, 2, 3, 3, 3, 4, 4, 4, 5, 6, 7, 7, 7, 7, 6, 6, 6, 5, 5, 5, 5, 6, 7, 7, 7, 8, 8, 8, 9, 10, 10, 10, 10, 9, 9, 9, 8, 8, 8, 8, 9, 10, 11, 11, 11, 12, 12, 12, 13, 14, 15, 15, 15, 15, 14, 14, 14, 13, 13, 13, 13, 14, 15, 15, 15, 15, 14, 14, 14, 13, 13, 13, 12, 12
Offset: 0

Views

Author

Rémy Sigrist, Apr 19 2020

Keywords

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(10) = a(15) = a(16) = a(17) = a(22) = 6.

Links

Crossrefs

Cf. A334188, A334221.

Programs

  • PARI
    See Links section.

Formula

A334188(A334221(n), a(n)) = n.

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.

Original entry on oeis.org

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

Views

Author

Rémy Sigrist, Apr 19 2020

Keywords

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

Crossrefs

Cf. A334188, A334220.

Programs

  • PARI
    See Links section.

Formula

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

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

Original entry on oeis.org

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

Views

Author

Rémy Sigrist, Apr 19 2020

Keywords

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(4) = a(5) = a(6) = a(11) = a(16) = a(17) = a(18) = 1.

Links

Crossrefs

Cf. A334188, A334223.

Programs

  • PARI
    See Links section.

Formula

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

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.

Original entry on oeis.org

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

Views

Author

Rémy Sigrist, Apr 19 2020

Keywords

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

Crossrefs

Cf. A334188, A334222.

Programs

  • PARI
    See Links section.

Formula

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

A334232 T(n, k) is the number of steps from the point (0, 0) to the point (k, n) along the H-order curve; a negative value corresponds to moving backwards; square array T(n, k), n, k >= 0 read by antidiagonals downwards.

Original entry on oeis.org

0, 1, -1, 4, 2, -2, 5, 3, -5, -3, 12, 6, -6, -4, -12, 13, 11, 7, -7, -11, -13, 16, 14, 10, 8, -8, -10, -14, 17, 15, 23, 9, -23, -9, -17, -15, 48, 18, 22, 24, -24, -22, -18, -16, -48, 49, 47, 19, 21, 25, -25, -21, -19, -47, -49, 52, 50, 46, 20, 28, 26, -26, -20
Offset: 0

Views

Author

Rémy Sigrist, Apr 19 2020

Keywords

Comments

The H-order curve is built as follows:
- we start we a unit square H_0 oriented counterclockwise, the origin being at the left bottom corner:
+---<---+
| |
v ^
| |
O--->---+
- the configuration H_{k+1} is obtained by connecting four copies of the configuration H_k as follows:
| | | |
. + + . . + + .
H_k ^ v H_k ^ v
. + + . . + + .
| | | |
-+->-+---+ +---+->-+- -+->-+ +-<-+ +->-+-
--> v ^
-+-<-+---+ +---+-<-+- -+-<-+ +->-+ +-<-+-
| | | |
. + + . . + + .
H_k ^ v H_k ^ v
. + + . . + + .
| | | |
- the H-order curve corresponds to the limit of H_k as k tends to infinity,
- the H-order curve visits once every lattice points with nonnegative coordinates and has a single connected component.

Examples

			Square array starts:
  n\k|    0    1    2    3    4    5    6    7
  ---+----------------------------------------
    0|    0....1    4....5   12...13   16...17
     |    |    |    |    |    |    |    |    |
    1|   -1    2....3    6   11   14...15   18
     |    |              |    |              |
    2|   -2   -5...-6    7   10   23...22   19
     |    |    |    |    |    |    |    |    |
    3|   -3...-4   -7    8....9   24   21...20
     |              |              |
    4|  -12..-11   -8  -23..-24   25   28...29
     |    |    |    |    |    |    |    |    |
    5|  -13  -10...-9  -22  -25   26...27   30
     |    |              |    |              |
    6|  -14  -17..-18  -21  -26  -29..-30   31
     |    |    |    |    |    |    |    |    |
    7|  -15..-16  -19..-20  -27..-28  -31   32

Links

Crossrefs

See A334188 for a similar sequence.
See A334233, A334234, A334235 and A334236 for the coordinates of the curve.

Programs

  • PARI
    See Links section.
Showing 1-5 of 5 results.

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