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 1-8 of 8 results.

A071339 a(n) = the maximum number of lattice points touched by an origin-centered circle with radius <= n.

Original entry on oeis.org

1, 4, 4, 8, 8, 12, 12, 12, 12, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 36, 36, 36
Offset: 0

Views

Author

Hugo Pfoertner, May 22 2002

Keywords

Examples

			a(5 to 8)=12 because the circle with radius 5 touches 12 lattice points: (+-1,+-2), (+-2,+-1), (+-5,0), (0,+-5); but no circle touches more, until the radius is sqrt(65).

Links

Crossrefs

Cf. A004018, A071339-A071347, A071383-A071385.

Formula

a(n) = max(i=0 to n^2) A004018(i)

Extensions

Edited by Don Reble, Nov 06 2005

A071342 a(n) = the maximum number of lattice points touched by an origin-centered sphere with radius <= n.

Original entry on oeis.org

6, 12, 30, 48, 48, 72, 96, 96, 120, 144, 168, 168, 192, 240, 240, 240, 264, 312, 336, 336, 336, 384, 384, 384, 408, 432, 480, 480, 504, 528, 552, 552, 552, 672, 672, 696, 720, 720, 720, 720, 768, 768, 816, 864, 864, 864, 936, 936, 936, 936, 936, 1008, 1008
Offset: 1

Views

Author

Hugo Pfoertner, May 22 2002

Keywords

Examples

			a(4 to 5)=48 because the sphere with radius sqrt(14) touches 48 lattice points; but no sphere touches more, until the radius is sqrt(26).

Crossrefs

Cf. A005875, A071339-A071347.

Programs

Formula

a(n) = max(i=0 to n^2) A005875(i)

Extensions

Edited by Don Reble, Nov 06 2005

A071344 a(n) = greatest 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, 21, 29, 41, 62, 74, 89, 101, 134, 161, 194, 209, 230, 269, 314, 341, 374, 425, 446, 521, 569, 614, 629, 689, 761, 794, 866, 941, 941, 941, 1154, 1154, 1286, 1361, 1361, 1454, 1454, 1634, 1634, 1781, 1889, 1889, 2054, 2141, 2246, 2246
Offset: 1

Views

Author

Hugo Pfoertner, May 22 2002

Keywords

Examples

			a(4)=21 because the largest sphere with radius <= 4 to touch A071342(4)=48 points has radius sqrt(21).

Crossrefs

Cf. A071339-A071347.

Programs

Extensions

Edited by Don Reble, Nov 06 2005

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

A071345 a(n) = the maximum number of lattice points touched by an origin-centered 4d-sphere with radius <= n.

Original entry on oeis.org

8, 32, 104, 192, 312, 576, 768, 960, 1344, 1872, 1920, 2496, 2976, 3072, 4608, 4608, 5760, 5760, 6912, 8064, 8064, 9672, 10368, 11520, 11520, 14976, 14976, 14976, 17424, 17784, 18432, 22464, 23808, 23808, 26208, 26208, 29760, 29952, 32832
Offset: 1

Views

Author

Hugo Pfoertner, May 22 2002

Keywords

Examples

			a(4)=192 because the 4d-sphere with radius sqrt(14) touches 192 lattice points.

Crossrefs

Cf. A000118, A071339-A071347.

Programs

Formula

a(n) = max(1=0 to n^2) A000118(i)

Extensions

Edited by Don Reble, Nov 06 2005

A071340 a(n) = least positive r <= n such that the origin-centered circle of radius sqrt(r) touches A071339(n) lattice points.

Original entry on oeis.org

0, 1, 1, 5, 5, 25, 25, 25, 25, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 325, 325, 325, 325, 325, 325, 325, 325, 325, 325, 325, 325, 325, 325, 325, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1105
Offset: 0

Views

Author

Hugo Pfoertner, May 22 2002

Keywords

Examples

			a(4)=5 because the smallest circle to touch A071339(4)=8 points has radius sqrt(5).

Links

Crossrefs

Cf. A071339-A071347.

Programs

Extensions

Edited by Don Reble, Nov 06 2005

A071346 a(n) = least positive r <= n, such that the origin-centered 4d-sphere of radius sqrt(r) touches A071345(n) lattice points.

Original entry on oeis.org

1, 3, 9, 14, 18, 30, 42, 54, 78, 90, 114, 126, 150, 186, 210, 210, 270, 270, 330, 390, 390, 450, 510, 570, 570, 630, 630, 630, 810, 882, 930, 990, 1050, 1050, 1170, 1170, 1350, 1386, 1470, 1530, 1650, 1710, 1710, 1890, 1890, 1890, 1890, 2250, 2310
Offset: 1

Views

Author

Hugo Pfoertner, May 22 2002

Keywords

Examples

			a(4)=14 because the smallest 4d-sphere to touch A071345(5)=192 points has radius sqrt(14).

Crossrefs

Cf. A071339-A071347.

Programs

Extensions

Edited by Don Reble, Nov 06 2005

A071341 a(n) = greatest positive r <= n, such that the origin-centered circle of radius sqrt(r) touches A071339(n) lattice points.

Original entry on oeis.org

0, 1, 4, 5, 13, 25, 25, 25, 50, 65, 85, 85, 130, 145, 185, 221, 250, 265, 305, 325, 325, 425, 425, 425, 425, 425, 650, 725, 725, 725, 850, 925, 925, 1025, 1105, 1105, 1105, 1105, 1105, 1105, 1105, 1625, 1625, 1625, 1885, 1885, 1885, 2125, 2210
Offset: 0

Views

Author

Hugo Pfoertner, May 22 2002

Keywords

Examples

			a(4)=13 because the largest circle with radius <= 4 to touch A071339(4)=8 points has radius sqrt(13).

Crossrefs

Cf. A071339-A071347.

Programs

Extensions

Edited by Don Reble, Nov 06 2005
Showing 1-8 of 8 results.

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