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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.

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A166041 Permutation of nonnegative integers: a(n) tells which integer is in the same position in the square array A163357 as where n is located in the array A163334.

Original entry on oeis.org

0, 1, 14, 13, 2, 3, 4, 7, 8, 11, 30, 29, 18, 17, 12, 15, 16, 19, 20, 21, 234, 233, 22, 23, 24, 25, 230, 229, 26, 27, 36, 37, 218, 217, 38, 39, 34, 33, 52, 53, 32, 35, 28, 31, 10, 9, 6, 5, 58, 57, 54, 55, 56, 59, 60, 61, 50, 49, 62, 63, 64, 67, 68, 69, 122, 123, 44, 47, 48
Offset: 0

Views

Author

Antti Karttunen, Oct 06 2009

Keywords

Comments

Fixed points are quite rare: A165465.

Examples

			The top left 9 X 9 corner of A163334:
   0  1  2 15 16 17 18 19 20
   5  4  3 14 13 12 23 22 21
   6  7  8  9 10 11 24 25 26
  47 46 45 44 43 42 29 28 27
  48 49 50 39 40 41 30 31 32
  53 52 51 38 37 36 35 34 33
  54 55 56 69 70 71 72 73 74
  59 58 57 68 67 66 77 76 75
  60 61 62 63 64 65 78 79 80
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
9 is in position (2,3) in A163334, while A163357(2,3) = 11. Thus a(9) = 11.

Links

Crossrefs

Inverse: A166042. a(n) = A163357(A163335(n)) = A163359(A163337(n)). Cf. also A166043.

A166043 Permutation of nonnegative integers: a(n) tells which integer is in the same position in the square array A163357 as where n is located in the array A163336.

Original entry on oeis.org

0, 3, 4, 7, 2, 1, 14, 13, 8, 9, 54, 55, 56, 57, 6, 5, 58, 59, 60, 63, 64, 67, 62, 61, 50, 49, 68, 69, 48, 51, 46, 47, 122, 123, 44, 45, 34, 35, 28, 31, 32, 33, 52, 53, 10, 11, 12, 15, 16, 17, 30, 29, 18, 19, 20, 23, 24, 25, 22, 21, 234, 233, 230, 229, 218, 217, 38, 37, 26
Offset: 0

Views

Author

Antti Karttunen, Oct 06 2009

Keywords

Comments

Fixed points are quite rare: A165467.

Examples

			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
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
3 is in position (2,1) in A163336, while A163357(2,1) = 7. Thus a(3) = 7.

Links

Crossrefs

Inverse: A166044. a(n) = A163357(A163337(n)) = A163359(A163335(n)). Cf. also A166041.

A166042 Permutation of nonnegative integers: a(n) tells which integer is in the same position in the square array A163334 as where n is located in the array A163357.

Original entry on oeis.org

0, 1, 4, 5, 6, 47, 46, 7, 8, 45, 44, 9, 14, 3, 2, 15, 16, 13, 12, 17, 18, 19, 22, 23, 24, 25, 28, 29, 42, 11, 10, 43, 40, 37, 36, 41, 30, 31, 34, 35, 72, 73, 76, 77, 66, 71, 70, 67, 68, 57, 56, 69, 38, 39, 50, 51, 52, 49, 48, 53, 54, 55, 58, 59, 60, 425, 424, 61, 62, 63, 422
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 A163334:
   0  1  2 15 16 17 18 19 20
   5  4  3 14 13 12 23 22 21
   6  7  8  9 10 11 24 25 26
  47 46 45 44 43 42 29 28 27
  48 49 50 39 40 41 30 31 32
  53 52 51 38 37 36 35 34 33
  54 55 56 69 70 71 72 73 74
  59 58 57 68 67 66 77 76 75
  60 61 62 63 64 65 78 79 80
9 is in position (3,2) in A163357, while A163334(3,2) = 45. Thus a(9) = 45.

Links

Crossrefs

Inverse: A166041. a(n) = A163334(A163358(n)) = A163336(A163360(n)). Fixed points: A165465. Cf. also A166044.

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.

Links

Crossrefs

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

A163365 Row sums of A163357 and A163359.

Original entry on oeis.org

0, 4, 20, 40, 100, 172, 248, 336, 568, 820, 1100, 1400, 1692, 2012, 2352, 2720, 3632, 4580, 5572, 6600, 7700, 8844, 10024, 11248, 12392, 13588, 14844, 16152, 17484, 18876, 20320, 21824, 25440, 29124, 32884, 36712, 40644, 44652, 48728, 52880
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Comments

All terms seem to be divisible by 4. Cf. A163477.

Links

Crossrefs

Cf. A163357, A163359.

Programs

  • Mathematica
    nn = 7; s[{n_, k_}, {m_}] := (a[k, n] = m - 1); MapIndexed[s, List @@ HilbertCurve[nn][[1]]]; Total /@ Table[a[n - k, k], {n, 0, nn^2}, {k, n, 0, -1}] (* Michael De Vlieger, Nov 01 2022, after Jean-François Alcover at A163357 *)

A163482 Row 0 of A163357 (column 0 of A163359).

Original entry on oeis.org

0, 1, 14, 15, 16, 19, 20, 21, 234, 235, 236, 239, 240, 241, 254, 255, 256, 259, 260, 261, 314, 315, 316, 319, 320, 321, 334, 335, 336, 339, 340, 341, 3754, 3755, 3756, 3759, 3760, 3761, 3774, 3775, 3776, 3779, 3780, 3781, 3834, 3835, 3836, 3839
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Crossrefs

Cf. A163483.

A163483 Row 0 of A163359 (column 0 of A163357).

Original entry on oeis.org

0, 3, 4, 5, 58, 59, 60, 63, 64, 65, 78, 79, 80, 83, 84, 85, 938, 939, 940, 943, 944, 945, 958, 959, 960, 963, 964, 965, 1018, 1019, 1020, 1023, 1024, 1025, 1038, 1039, 1040, 1043, 1044, 1045, 1258, 1259, 1260, 1263, 1264, 1265, 1278, 1279, 1280, 1283
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Crossrefs

Cf. A163482.

A165464 Squared distance between n's location in A163334 array and A163357 array.

Original entry on oeis.org

0, 0, 2, 4, 2, 4, 2, 0, 0, 2, 2, 4, 4, 4, 2, 0, 0, 2, 2, 4, 4, 2, 0, 0, 0, 0, 2, 4, 4, 2, 8, 10, 16, 16, 4, 2, 2, 10, 16, 10, 8, 8, 20, 20, 20, 18, 18, 32, 18, 10, 4, 2, 4, 10, 8, 2, 2, 10, 10, 4, 4, 4, 2, 10, 16, 26, 20, 10, 2, 4, 10, 18, 32, 32, 50, 52, 52, 34, 40, 58, 80, 80, 106, 146
Offset: 0

Views

Author

Antti Karttunen, Oct 06 2009

Keywords

Comments

Equivalently, squared distance between n's location in A163336 array and A163359 array. See example at A166041.

Links

Crossrefs

Positions of zeros: A165465. See also A165466, A163897, A163900.

Formula

a(n) = A000290(abs(A163529(n)-A059252(n))) + A000290(abs(A163528(n)-A059253(n))).

A163477 Row sums of A163357 and A163359 divided by 4.

Original entry on oeis.org

0, 1, 5, 10, 25, 43, 62, 84, 142, 205, 275, 350, 423, 503, 588, 680, 908, 1145, 1393, 1650, 1925, 2211, 2506, 2812, 3098, 3397, 3711, 4038, 4371, 4719, 5080, 5456, 6360, 7281, 8221, 9178, 10161, 11163, 12182, 13220, 14310, 15421, 16555, 17710
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Links

Crossrefs

Cf. A163357, A163359.

Programs

  • Mathematica
    nn = 8; s[{n_, k_}, {m_}] := (a[k, n] = m - 1); MapIndexed[s, List @@ HilbertCurve[nn][[1]]]; Floor[1/4*Map[Total, Table[a[n - k, k], {n, 0, nn^2}, {k, n, 0, -1}]]] (* Michael De Vlieger, Nov 01 2022, after Jean-François Alcover at A163357 *)

Formula

a(n) = floor(A163365(n)/4) (floor probably unnecessary).

A163334 Peano curve in an n X n grid, starting rightwards from the top left corner, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ... .

Original entry on oeis.org

0, 1, 5, 2, 4, 6, 15, 3, 7, 47, 16, 14, 8, 46, 48, 17, 13, 9, 45, 49, 53, 18, 12, 10, 44, 50, 52, 54, 19, 23, 11, 43, 39, 51, 55, 59, 20, 22, 24, 42, 40, 38, 56, 58, 60, 141, 21, 25, 29, 41, 37, 69, 57, 61, 425, 142, 140, 26, 28, 30, 36, 70, 68, 62, 424, 426, 143, 139
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Examples

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

Links

Crossrefs

Transpose: A163336. Inverse: A163335. One-based version: A163338. Row sums: A163342. Row 0: A163480. Column 0: A163481. Central diagonal: A163343.
See also: A163528-A163529, A163531, A163534, A163536, A163897.
See A163357 and A163359 for the Hilbert curve.

Programs

  • Mathematica
    b[{n_, k_}, {m_}] := (A[k, n] = m - 1);
MapIndexed[b, List @@ PeanoCurve[4][[1]]];
Table[A[n - k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Mar 07 2021 *)

Formula

a(n) = A163332(A163328(n)).

Extensions

Links to further derived sequences added by Antti Karttunen, Sep 21 2009
Name corrected by Kevin Ryde, Aug 22 2020
Previous Showing 11-20 of 38 results. Next

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