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.

A071611 Number of points (i,j,k) on the surface of a sphere around (0,0,0) with squared radius A071609(n).

Original entry on oeis.org

6, 12, 24, 30, 48, 72, 96, 120, 144, 168, 192, 240, 264, 312, 336, 384, 408, 432, 480, 504, 528, 552, 576, 600, 672, 696, 720, 768, 816, 864, 936, 1008, 1032, 1056, 1104, 1200, 1248, 1296, 1344, 1440, 1512, 1584, 1680, 1704, 1752, 1848, 1920, 2016
Offset: 1

Views

Author

Hugo Pfoertner, May 25 2002

Keywords

Comments

a(n) is the number of lattice points on a sphere around (0,0,0) with r^2 = A071609(n).

Examples

			A sphere with radius 1 has 6 lattice points on its surface, so a(1)=6. A sphere with r=sqrt(2) passes through 12 lattice points of the shape (1,1,0), so a(2)=12. A sphere with r=sqrt(5) passes through 24 lattice points with shape (2,1,0), so a(3)=24. A sphere with r=sqrt(9) passes through 6 lattice points of shape (3,0,0) and through 24 lattice points of shape (2,2,1), so a(4)=6+24=30.

Links

Crossrefs

Cf. A005875, A071342-A071344, A071609, A071610.

Formula

a(n) = A005875(A071609(n)). - Daniel Suteu, Aug 13 2021

A076180 Indices of spheres mentioned in A071609.

Original entry on oeis.org

1, 2, 5, 8, 13, 23, 35, 63, 76, 86, 123, 163, 226, 264, 287, 374, 514, 523, 576, 664, 715, 787, 924, 927, 963, 1074, 1137, 1364, 1487, 1576, 1786, 2176, 2475, 2614, 2837, 2877, 2925, 3536, 3576, 4025, 4487, 4638, 5215, 6026, 6527, 6726, 6774
Offset: 1

Views

Author

Hugo Pfoertner, Nov 01 2002

Keywords

Examples

			a(7)=35 because A000378(35)=A071609(7)=41

References

  • J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, Table 4.3, p. 107.

Links

Crossrefs

Cf. A000378, A005875, A071609.

Formula

a(n) = k for which A000378(k) = A071609(n)

A071343 a(n) = least positive r <= n, such that the origin-centered sphere of radius sqrt(r) touches A071342(n) lattice points.

Original entry on oeis.org

1, 2, 9, 14, 14, 26, 41, 41, 74, 89, 101, 101, 146, 194, 194, 194, 269, 314, 341, 341, 341, 446, 446, 446, 614, 626, 689, 689, 794, 854, 941, 941, 941, 1154, 1154, 1286, 1361, 1361, 1361, 1361, 1634, 1634, 1781, 1889, 1889, 1889, 2141, 2141
Offset: 1

Views

Author

Hugo Pfoertner, May 22 2002

Keywords

Examples

			a(5)=14 because the smallest sphere to touch A071342(5)=48 points has radius sqrt(14).

Crossrefs

Cf. A071339, A071340, A071341, A071342, A071343, A071344, A071345, A071346, A071347. A071609.

Programs

Extensions

Edited by Don Reble, Nov 06 2005

A071610 Integer radii of the spheres around (0,0,0) that contain record numbers of lattice points.

Original entry on oeis.org

1, 2, 3, 3, 4, 6, 7, 9, 10, 11, 13, 14, 17, 18, 19, 22, 25, 26, 27, 29, 30, 31, 34, 34, 34, 36, 37, 41, 43, 44, 47, 52, 55, 56, 59, 59, 60, 66, 66, 70, 74, 75, 80, 86, 89, 90, 91, 94, 100, 103, 104, 109, 115, 115, 119, 125, 134, 141, 146, 153, 153, 157, 168, 171
Offset: 1

Views

Author

Hugo Pfoertner, May 25 2002

Keywords

Comments

Multiple entries indicate that there is more than one covered sphere with an increase in the number of hit lattice points within a radius difference of 1.

Crossrefs

Cf. A071342, A071343, A071344, A071609, A071611.

Formula

a(n) = ceiling(A071609(n)^(1/2)).
Showing 1-4 of 4 results.

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

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