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 1-6 of 6 results.

A163357 Hilbert curve in N X N grid, starting rightwards from the top-left corner, listed by descending antidiagonals.

Original entry on oeis.org

0, 1, 3, 14, 2, 4, 15, 13, 7, 5, 16, 12, 8, 6, 58, 19, 17, 11, 9, 57, 59, 20, 18, 30, 10, 54, 56, 60, 21, 23, 29, 31, 53, 55, 61, 63, 234, 22, 24, 28, 32, 52, 50, 62, 64, 235, 233, 25, 27, 35, 33, 51, 49, 67, 65, 236, 232, 230, 26, 36, 34, 46, 48, 68, 66, 78, 239, 237, 231
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Examples

			The top left 8 X 8 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...):
   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

Links

Crossrefs

Transpose: A163359. Inverse: A163358. One-based version: A163361. Row sums: A163365. Row 0: A163482. Column 0: A163483. Central diagonal: A062880. See also A163334 & A163336 for the Peano curve.
See also: A163540, A163542, A163547, A163898, A163899, A163900, A163538, A163539, A163904, A163907, A163917.

Programs

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

Formula

a(n) = A163355(A054238(n)).

Extensions

Links to further derived sequences added by Antti Karttunen, Sep 21 2009

A163901 The positions i where A163355(i) = i, that is, the fixed points of permutation A163355.

Original entry on oeis.org

0, 1, 16, 20, 21, 256, 260, 261, 320, 321, 336, 340, 341, 4096, 4100, 4101, 4160, 4161, 4176, 4180, 4181, 5120, 5121, 5136, 5140, 5141, 5376, 5380, 5381, 5440, 5441, 5456, 5460, 5461, 65536, 65540, 65541, 65600, 65601, 65616, 65620, 65621
Offset: 0

Views

Author

Antti Karttunen, Sep 19 2009

Keywords

Comments

Alternatively, the positions of zeros in A163900.

Crossrefs

a(n) = A000695(A165404(n)). Same sequence in base-4: A165406. See also A163902, A163903, A163910.

A163898 Array A(i,j) giving the square of distance from (i,j) to the location where A054238(i,j) is situated in array A163357(i,j), 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, 0, 1, 8, 1, 4, 18, 5, 2, 9, 0, 5, 2, 5, 16, 2, 1, 2, 9, 10, 25, 0, 1, 4, 9, 16, 17, 36, 0, 1, 4, 9, 16, 25, 36, 49, 128, 1, 2, 1, 10, 9, 10, 25, 64, 162, 113, 4, 5, 18, 5, 4, 5, 50, 81, 128, 113, 100, 9, 10, 5, 10, 1, 64, 65, 100, 128, 113, 100, 89, 16, 17, 20, 25, 64, 81, 100
Offset: 0

Views

Author

Antti Karttunen, Sep 19 2009

Keywords

Examples

			The top left 8 X 8 corner of this array:
   0  0  8 18  0  2  0  0
   1  1  5  5  1  1  1  1
   4  2  2  2  4  4  2  4
   9  5  9  9  9  1  5  9
  16 10 16 16 10 18 10 16
  25 17 25  9  5  5 17 25
  36 36 10  4 10 20 36 36
  49 25  5  1 25 29 25 49

Links

Crossrefs

a(n) = A163900(A054238(n)). Positions of zeros: A165403. See also A163899, A163904.

A163899 Array A(i,j) giving the square of distance from (i,j) to the location where A163357(i,j) is situated in array A054238(i,j), 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, 0, 1, 9, 1, 8, 9, 2, 5, 18, 0, 2, 4, 5, 25, 1, 2, 5, 2, 20, 29, 0, 1, 5, 9, 17, 10, 36, 0, 1, 4, 9, 16, 25, 36, 49, 225, 1, 4, 2, 16, 10, 5, 25, 128, 225, 170, 4, 1, 17, 10, 5, 18, 113, 162, 196, 170, 125, 9, 16, 25, 5, 10, 128, 113, 149, 225, 170, 125, 90, 16, 9, 4, 1, 128
Offset: 0

Views

Author

Antti Karttunen, Sep 19 2009

Keywords

Examples

			The top left 8x8 corner of this array:
+0 +0 +9 +9 +0 +1 +0 +0
+1 +1 +2 +2 +2 +1 +1 +1
+8 +5 +4 +5 +5 +4 +4 +4
18 +5 +2 +9 +9 +2 +1 +9
25 20 17 16 16 17 16 16
29 10 25 10 10 25 +9 25
36 36 +5 +5 +5 +4 36 36
49 25 18 10 +1 10 25 49

Links

Crossrefs

a(n) = A163900(A163357(n)). Positions of zeros: A165403. See also A163898, A163904.

A165466 Squared distance between n's location in A163334 array and A163359 array.

Original entry on oeis.org

0, 2, 2, 2, 2, 10, 10, 2, 0, 0, 2, 10, 20, 10, 10, 18, 32, 32, 50, 74, 100, 100, 72, 50, 32, 50, 50, 34, 20, 20, 16, 16, 16, 10, 4, 4, 2, 4, 8, 8, 8, 10, 20, 18, 20, 20, 26, 50, 50, 40, 20, 20, 20, 20, 32, 32, 34, 40, 58, 74, 100, 74, 74, 80, 80, 80, 52, 52, 50, 34, 34, 32
Offset: 0

Views

Author

Antti Karttunen, Oct 06 2009

Keywords

Comments

Equivalently, squared distance between n's location in A163336 array and A163357 array. See example at A166043.

Links

Crossrefs

Positions of zeros: A165467. See also A166043, A165464, A163897, A163900.

Formula

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

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))).
Showing 1-6 of 6 results.

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