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 1-10 of 10 results.

A382761 List of graphs that are squares, encoded as in A382754.

Original entry on oeis.org

0, 1, 2, 3, 8, 9, 15, 64, 65, 75, 76, 95, 127, 1024, 1025, 1043, 1044, 1079, 1207, 1208, 1247, 1279, 1535, 2047, 32768, 32769, 32803, 32804, 32871, 33383, 33384, 33424, 33455, 33519, 33689, 34543, 34687, 36863, 38639, 38640, 38673, 38711, 38719, 38783, 38911, 39423, 39935, 40959, 48638, 48639, 49151, 65535
Offset: 0

Views

Author

Pontus von Brömssen, Apr 05 2025

Keywords

Examples

			As an irregular triangle, where row n >= 0 contains A382181(n) terms:
     0;
     1;
     2,    3;
     8,    9,   15;
    64,   65,   75,   76,   95,  127;
  1024, 1025, 1043, 1044, 1079, 1207, 1208, 1247, 1279, 1535, 2047;
  ...

Crossrefs

Cf. A382181, A382194, A382754, A382762, A382763.

Formula

a(n) = A382754(A382762(n)).

A382762 List of graphs that are squares, encoded by their indices in A382754.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 17, 18, 19, 20, 24, 25, 32, 39, 40, 47, 49, 51, 52, 53, 54, 59, 60, 70, 89, 90, 99, 107, 117, 127, 144, 160, 170, 171, 172, 177, 182, 186, 191, 193, 195, 201, 204, 205, 206, 207, 208
Offset: 0

Views

Author

Pontus von Brömssen, Apr 05 2025

Keywords

Examples

			As an irregular triangle, where row n >= 0 contains A382181(n) terms:
   0;
   1;
   2,  3;
   4,  5,  7;
   8,  9, 12, 13, 17, 18;
  19, 20, 24, 25, 32, 39, 40, 47, 49, 51, 52;
  ...

Crossrefs

Cf. A382181, A382194, A382754, A382761, A382764.

A382763 a(n) is the code (in the encoding given by A382754) of the square of the graph with code A382754(n).

Original entry on oeis.org

0, 1, 2, 3, 8, 9, 15, 15, 64, 65, 75, 127, 75, 76, 95, 127, 127, 127, 127, 1024, 1025, 1043, 1207, 2047, 1043, 1044, 1079, 1207, 1208, 1279, 2047, 1207, 1207, 1247, 1535, 1535, 2047, 2047, 2047, 1207, 1208, 1279, 1535, 2047, 2047, 2047, 2047, 2047, 2047, 2047, 2047, 2047, 2047
Offset: 0

Views

Author

Pontus von Brömssen, Apr 05 2025

Keywords

Examples

			As an irregular triangle, where row n >= 0 contains A000088(n) terms:
   0;
   1;
   2,  3;
   8,  9, 15,  15;
  64, 65, 75, 127, 75, 76, 95, 127, 127, 127, 127;
  ...

Crossrefs

Cf. A000088, A382195, A382754, A382761, A382764.

Formula

a(n) = A382754(A382764(n)).

A382764 a(n) is the index in A382754 of the square of the graph with code A382754(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 7, 8, 9, 12, 18, 12, 13, 17, 18, 18, 18, 18, 19, 20, 24, 39, 52, 24, 25, 32, 39, 40, 49, 52, 39, 39, 47, 51, 51, 52, 52, 52, 39, 40, 49, 51, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52
Offset: 0

Views

Author

Pontus von Brömssen, Apr 05 2025

Keywords

Examples

			As an irregular triangle, where row n >= 0 contains A000088(n) terms:
  0;
  1;
  2, 3;
  4, 5,  7,  7;
  8, 9, 12, 18, 12, 13, 17, 18, 18, 18, 18;
  ...

Crossrefs

Cf. A000088, A382195, A382754, A382762, A382763.

A382756 a(n) is the graph corresponding to A076184(n), encoded as in A382754.

Original entry on oeis.org

1, 3, 11, 15, 71, 76, 77, 79, 94, 95, 127, 1039, 1052, 1053, 1055, 1082, 1083, 1086, 1087, 1208, 1209, 1211, 1215, 1150, 1151, 1231, 1244, 1245, 1247, 1278, 1279, 1519, 1535, 2047, 32799, 32828, 32829, 32831, 32888, 32889, 32890, 32891, 32894, 32895, 33400
Offset: 1

Views

Author

Pontus von Brömssen, Apr 04 2025

Keywords

Examples

			As an irregular triangle, where the first row contains 1 term and row n >= 2 contains A002494(n) terms:
   1;
   3;
  11, 15;
  71, 76, 77, 79, 94, 95, 127;
  ...

Crossrefs

Cf. A002494, A076184, A382754, A382757.

A382757 a(n) is the graph corresponding to A382754(n), encoded as in A076184.

Original entry on oeis.org

0, 0, 1, 0, 1, 3, 7, 0, 1, 3, 11, 7, 12, 13, 15, 30, 31, 63, 0, 1, 3, 11, 75, 7, 12, 13, 15, 76, 77, 79, 30, 31, 86, 87, 94, 95, 222, 223, 63, 116, 117, 119, 127, 235, 236, 237, 239, 254, 255, 507, 511, 1023, 0, 1, 3, 11, 75, 1099, 7, 12, 13, 15, 76, 77, 79
Offset: 1

Views

Author

Pontus von Brömssen, Apr 04 2025

Keywords

Comments

Any isolated vertices in the graphs are ignored (except for the 1-vertex graph).

Examples

			As an irregular triangle, where row n >= 1 contains A000088(n) terms:
  0;
  0, 1;
  0, 1, 3,  7;
  0, 1, 3, 11, 7, 12, 13, 15, 30, 31, 63;
  ...

Crossrefs

Cf. A000088, A076184, A382754, A382756.

A382758 Number of edges of the graph encoded by A382754(n).

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 3, 2, 3, 4, 4, 5, 6, 0, 1, 2, 3, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 5, 5, 6, 6, 7, 6, 4, 5, 6, 7, 6, 5, 6, 7, 7, 8, 8, 9, 10, 0, 1, 2, 3, 4, 5, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 6, 7, 6, 7, 6, 7, 7, 8
Offset: 0

Views

Author

Pontus von Brömssen, Apr 04 2025

Keywords

Examples

			As an irregular triangle, where row n >= 0 contains A000088(n) terms:
  0;
  0;
  0, 1;
  0, 1, 2, 3;
  0, 1, 2, 3, 3, 2, 3, 4, 4, 5, 6;
  ...

Crossrefs

Cf. A000088, A000120, A382191, A382754.

Formula

a(n) = A000120(A382754(n))-1 for n >= 1.

A382759 Number of connected components of the graph encoded by A382754(n).

Original entry on oeis.org

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

Views

Author

Pontus von Brömssen, Apr 04 2025

Keywords

Examples

			As an irregular triangle, where row n >= 0 contains A000088(n) terms:
  0;
  1;
  2, 1;
  3, 2, 1, 1;
  4, 3, 2, 1, 2, 2, 1, 1, 1, 1, 1;
  ...

Crossrefs

Cf. A000088, A382192, A382754.

A382760 Independence number of the graph encoded by A382754(n).

Original entry on oeis.org

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

Views

Author

Pontus von Brömssen, Apr 04 2025

Keywords

Examples

			As an irregular triangle, where row n >= 0 contains A000088(n) terms:
  0;
  1;
  2, 1;
  3, 2, 2, 1;
  4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1;
  ...

Crossrefs

Cf. A000088, A002024, A065120, A382754.

Formula

a(n) = A002024(A065120(A382754(n))) for n >= 1.

A382755 Irregular triangle read by rows: Let k encode the edges of an n-vertex graph by taking edges (u,v), with u < v, in lexicographic order ((0,1), ..., (0,n-1), (1,2), ..., (1,n-1), ..., (n-1,n)) and adding each edge to the graph if the corresponding binary digit of k (starting with the least significant digit) is 1. T(n,k) is the smallest nonnegative integer that encodes the same unlabeled n-vertex graph as k, 0 <= k < n*(n-1)/2.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 1, 3, 1, 3, 3, 7, 0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 11, 12, 13, 13, 15, 1, 3, 12, 13, 3, 11, 13, 15, 3, 7, 13, 15, 13, 15, 30, 31, 1, 12, 3, 13, 3, 13, 11, 15, 3, 13, 7, 15, 13, 30, 15, 31, 3, 13, 13, 30, 7, 15, 15, 31, 11, 15, 15, 31, 15, 31, 31, 63
Offset: 0

Views

Author

Pontus von Brömssen, Apr 04 2025

Keywords

Comments

In the encoding given by A382754, the code of the graph corresponding to T(n,k) is 2^(n*(n-1)/2) + T(n,k) if n > 0.
The first case where a row is not an initial segment of the next row is T(4,11) = 11 != 7 = T(5,11).

Examples

			Triangle begins:
  0;
  0;
  0, 1;
  0, 1, 1, 3, 1, 3, 3, 7;
  ...
For n = 5, k = 11, 11 is 1011 in binary, which encodes the 5-vertex graph with edges (0,1), (0,2), and (0,4) (3 being an isolated vertex). The smallest code for an isomorphic graph is obtained by substituting the edge (0,3) for (0,4), resulting in the code 111 in binary, i.e., T(5,11) = 7.

Crossrefs

Cf. A382281, A382754.

Formula

T(n,k) <= k with equality if and only if 2^(n*(n-1)/2) + k is in A382754.
Showing 1-10 of 10 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.