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 1-4 of 4 results.

A084827 Maximum number of spheres of volume one that can be packed in a sphere of volume n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 6, 6, 6, 7, 8, 8, 9, 9, 10, 10, 12, 12, 13, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 19, 20, 21, 21, 21, 22, 22, 23, 23, 23, 25, 25, 26, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 34, 35, 36, 36, 38, 38, 38, 38, 39, 39, 40, 40, 42, 42, 42, 43, 43, 44
Offset: 1

Views

Author

Hugo Pfoertner, Jun 09 2003

Keywords

Comments

Higher terms of the sequence are only conjectures derived from numerical results. The first 12 arrangements are identical with the solutions of the Tammes problem (see A080865).

Examples

			a(10)=2 because a sphere of volume 10 is slightly too small to cover 3 mutually touching spheres of volume 1. a(27)=13 because the arrangement of 12 spheres plus one central sphere needs exactly a sphere with R=3*r to be contained.

Links

Crossrefs

Cf. A084828, A084829, A084824, A080865.

Extensions

More terms from Hugo Pfoertner, May 09 2005

A084825 Maximum number of spheres of diameter one that can be packed in a cube of edge length n.

Original entry on oeis.org

1, 8, 27, 66
Offset: 1

Views

Author

Hugo Pfoertner, Jun 12 2003

Keywords

Comments

From an extrapolation of Dave Boll's numerical results a(4)~=66 and a(5)~=141 are estimated values for the next terms.
However, E. Specht's data suggest a(5)=135. - Hugo Pfoertner, Jul 08 2025

Examples

			a(3)=27 because there is no known better arrangement than the 3*3*3 cubic one that would allow packing more than 27 spheres into a cube of edge length 3.

Links

Crossrefs

Cf. A084824, A084828, A084617.

Extensions

a(4) from Hugo Pfoertner, May 21 2011

A084826 Best packing of m>1 equal spheres in a cube setting a new density record.

Original entry on oeis.org

2, 3, 4, 6, 7, 8, 31, 32, 48, 60, 61, 62, 63
Offset: 1

Views

Author

Hugo Pfoertner, Jun 12 2003

Keywords

Comments

The terms >=31 are only conjectures found by numerical experimentation. In the table given at the Pfoertner link, the densities are given relative to the density of the cubic lattice packing (Pi/6). The first known arrangement with higher density than that of the cubic lattice packing was found for m=31 spheres. In the region 8

References

Links

Crossrefs

Cf. A084824, A084829, A051657.

Extensions

More terms from Hugo Pfoertner, Oct 03 2015

A228881 Minimum number of spheres touching a wall of the container in the densest packing of n equal spheres into a cube.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 10, 10, 13, 14, 14, 13, 16, 17, 12, 14, 8, 12, 20, 15, 19, 20, 26, 22, 25, 26, 27, 28, 22
Offset: 1

Views

Author

Hugo Pfoertner, Sep 13 2013

Keywords

Comments

Spheres that are not part of the rigid framework, "rattlers", are always assumed not to touch the walls of the container cube.
If optimal configurations can be obtained by taking away an arbitrary sphere from a configuration with a higher sphere count, a sphere touching the container wall is chosen.

Examples

			The first configuration in which there is an inner sphere not touching the walls occurs for n = 9, with 8 spheres in the corners of the cube and one sphere in the center of the cube. Therefore a(9) = 8.

Links

Crossrefs

Cf. A084824.

Extensions

a(25)-a(33) from Hugo Pfoertner, Mar 23 2021
Showing 1-4 of 4 results.

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