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.

Previous Showing 31-36 of 36 results.

A163338 Peano curve in an N x N grid, one-based, starting rightwards from the top-left corner.

Original entry on oeis.org

1, 2, 6, 3, 5, 7, 16, 4, 8, 48, 17, 15, 9, 47, 49, 18, 14, 10, 46, 50, 54, 19, 13, 11, 45, 51, 53, 55, 20, 24, 12, 44, 40, 52, 56, 60, 21, 23, 25, 43, 41, 39, 57, 59, 61, 142, 22, 26, 30, 42, 38, 70, 58, 62, 426, 143, 141, 27, 29, 31, 37, 71, 69, 63, 425, 427, 144, 140
Offset: 1

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Comments

See the comments at A163334.

Crossrefs

Inverse: A163339. Transpose: A163340.

Formula

a(n) = A163334(n-1)+1

Extensions

Name corrected by Kevin Ryde, Aug 28 2020

A166044 Permutation of nonnegative integers: a(n) tells which integer is in the same position in the square array A163336 as where n is located in the array A163357.

Original entry on oeis.org

0, 5, 4, 1, 2, 15, 14, 3, 8, 9, 44, 45, 46, 7, 6, 47, 48, 49, 52, 53, 54, 59, 58, 55, 56, 57, 68, 69, 38, 51, 50, 39, 40, 41, 36, 37, 70, 67, 66, 71, 72, 77, 76, 73, 34, 35, 30, 31, 28, 25, 24, 29, 42, 43, 10, 11, 12, 13, 16, 17, 18, 23, 22, 19, 20, 141, 140, 21, 26, 27, 134
Offset: 0

Views

Author

Antti Karttunen, Oct 06 2009

Keywords

Examples

			The top left 8 X 8 corner of A163357:
   0  1 14 15 16 19 20 21
   3  2 13 12 17 18 23 22
   4  7  8 11 30 29 24 25
   5  6  9 10 31 28 27 26
  58 57 54 53 32 35 36 37
  59 56 55 52 33 34 39 38
  60 61 50 51 46 45 40 41
  63 62 49 48 47 44 43 42
The top left 9 X 9 corner of A163336:
   0  5  6 47 48 53 54 59 60
   1  4  7 46 49 52 55 58 61
   2  3  8 45 50 51 56 57 62
  15 14  9 44 39 38 69 68 63
  16 13 10 43 40 37 70 67 64
  17 12 11 42 41 36 71 66 65
  18 23 24 29 30 35 72 77 78
  19 22 25 28 31 34 73 76 79
  20 21 26 27 32 33 74 75 80
12 is in position (1,3) in A163357, while A163336(1,3) = 46. Thus a(12) = 46.
		

Crossrefs

Inverse: A166043. a(n) = A163336(A163358(n)) = A163334(A163360(n)). Fixed points: A165467. Cf. also A166042.

A163333 Self-inverse permutation of integers: A163327-conjugate of A163332.

Original entry on oeis.org

0, 7, 2, 3, 4, 5, 6, 1, 8, 69, 64, 71, 66, 67, 68, 63, 70, 65, 18, 25, 20, 21, 22, 23, 24, 19, 26, 29, 34, 27, 32, 31, 30, 35, 28, 33, 44, 37, 42, 41, 40, 39, 38, 43, 36, 47, 52, 45, 50, 49, 48, 53, 46, 51, 54, 61, 56, 57, 58, 59, 60, 55, 62, 15, 10, 17, 12, 13, 14, 9, 16, 11
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Comments

The integers [0,(9^k)-1] are confined to range [0,(9^k)-1].

Crossrefs

a(n) = A163327(A163332(A163327(n))). A163334 & A163336 give two variants of the Peano curve in an N x N grid. Cf. also A163355.

A262174 Sierpiński arrowhead curve as a triangular array starting leftward from the top, read by rows.

Original entry on oeis.org

1, 2, 0, 0, 3, 4, 9, 8, 0, 5, 10, 0, 7, 6, 0, 0, 11, 0, 0, 23, 24, 13, 12, 0, 0, 22, 0, 25, 14, 0, 17, 18, 0, 21, 26, 0, 0, 15, 16, 0, 19, 20, 0, 27, 28, 69, 68, 0, 0, 0, 0, 0, 0, 0, 29, 70, 0, 67, 0, 0, 0, 0, 0, 31, 30, 0, 0, 71, 66, 0, 0, 0, 0, 0, 32, 0, 35, 36
Offset: 1

Views

Author

Max Barrentine, Sep 13 2015

Keywords

Comments

The triangle up to the (1 + 2^n)th row is the n-th iteration of the curve, rotated such that the curve begins at the top and continues down to the left.
As this is not a space-filling curve, not all points on the triangular lattice are reached by the curve; these points are given the value 0.

Examples

			The first 5 rows of this triangle show how this curve begins (connect the terms in numerical order):
            1;
          2,  0;
        0,  3,  4;
      9,  8,  0,  5;
   10,  0,  7,  6,  0;
   ...
		

Crossrefs

See also A163357, A163334, and A054238 for other fractal curves.

A265318 Fibonacci word fractal in an n X n grid, starting downwards from the top-left corner, listed antidiagonally.

Original entry on oeis.org

1, 0, 2, 5, 3, 0, 6, 4, 0, 0, 7, 0, 0, 0, 0, 0, 8, 10, 0, 0, 20, 0, 0, 9, 11, 0, 19, 21, 0, 0, 0, 0, 12, 18, 0, 22, 0, 0, 0, 0, 13, 0, 17, 23, 0, 0, 0, 0, 0, 0, 14, 16, 0, 24, 26, 0, 0, 0, 0, 0, 0, 15, 0, 0, 25, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 83
Offset: 1

Views

Author

Max Barrentine, Dec 06 2015

Keywords

Comments

The n-th iteration of this curve ends at the n-th Fibonacci number.
As this is not a space-filling curve, not all points on the grid are reached by the curve; these points are given the value 0.

Examples

			The top left corner of the array shows how this curve begins (connect the terms in numerical order):
   1   0   5   6   7
   2   3   4   0   8
   0   0   0  10   9
   0   0   0  11   0
   0   0   0  12  13
  20  19  18   0  14
  21   0  17  16  15
  22  23   0   0   0
   0  24   0   0   0
  26  25   0   0   0
  27   0  31  32  33
  28  29  30   0  34
		

Crossrefs

See also A163357, A163334, and A054238 for other fractal curves.

A323335 Square array T(n, k) read by antidiagonals upwards, n >= 0 and k >= 0: the point with coordinates X=k and Y=n is the T(n, k)-th term of the first type of Wunderlich curve.

Original entry on oeis.org

1, 2, 6, 3, 5, 7, 48, 4, 8, 16, 49, 47, 9, 15, 17, 54, 50, 46, 10, 14, 18, 55, 53, 51, 45, 11, 13, 19, 56, 60, 52, 44, 40, 12, 20, 24, 57, 59, 61, 43, 41, 39, 21, 23, 25, 462, 58, 62, 70, 42, 38, 30, 22, 26, 106, 463, 461, 63, 69, 71, 37, 31, 29, 27, 105, 107
Offset: 0

Views

Author

Rémy Sigrist, Jan 11 2019

Keywords

Comments

Each natural numbers appears once in the sequence.

Examples

			Array T(n, k) begins:
  n\k|   0   1   2   3   4   5   6   7   8
  ---+------------------------------------
  0  |   1   6---7  16--17--18--19  24--25
     |   |   |   |   |           |   |   |
  1  |   2   5   8  15--14--13  20  23  26
     |   |   |   |           |   |   |   |
  2  |   3---4   9--10--11--12  21--22  27
     |                                   |
  3  |  48--47--46--45  40--39  30--29--28
     |   |           |   |   |   |
  4  |  49--50--51  44  41  38  31--32--33
     |           |   |   |   |           |
  5  |  54--53--52  43--42  37--36--35--34
     |   |
  6  |  55  60--61  70--71--72--73  78--79
     |   |   |   |   |           |   |   |
  7  |  56  59  62  69--68--67  74  77  80
     |   |   |   |           |   |   |   |
  8  |  57--58  63--64--65--66  75--76  81
		

Crossrefs

See A163334 for a similar sequence.

Formula

T(A323259(n), A323258(n)) = n.
Previous Showing 31-36 of 36 results.