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.

A375151 Decimal expansion of the circumradius of a regular 9-gon with unit side length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 01 2024

Keywords

Examples

			1.46190220008154362611637720668314585193675283...

Links

Crossrefs

Cf. A375152 (apothem), A375153 (sagitta), A256853 (area).
Cf. circumradius of other polygons with unit side length: A020760 (triangle), A010503 (square), A300074 (pentagon), A374957 (heptagon), A285871 (octagon), A001622 (10-gon), A375190 (11-gon), A188887 (12-gon)
Cf. A019879, A121602, A272488.

Programs

Formula

Equals csc(Pi/9)/2 = A121602/2.
Equals 1/(2*sin(Pi/9)) = 1/A272488.
Equals A375152/cos(Pi/9) = A375152/A019879.
Equals A375152 + A375153.
Largest of the 6 real-valued roots of 3*x^6-9*x^4+6*x^2-1=0. - R. J. Mathar, Aug 29 2025

A121603 Numbers n such that the radius of the smallest circle into which n unit circles can be packed is 1 + csc(Pi/k), where k >= 2 is an integer.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 11
Offset: 1

Views

Author

Rick L. Shepherd, Aug 09 2006

Keywords

Comments

Corresponding k values are in A121604. For these n, the centers of k unit circles can form a regular k-gon with sides of length 2 centered at the center of the larger circle. From the diagrams in the link it appears likely that 13,18,19 are the next three terms.

Examples

			See A121602 for the case n=11 involving a 9-gon.

Links

Crossrefs

Cf. A121604, A121570, A121598, A121601, A121602.

A121604 Numbers k such that the radius of the smallest circle into which A121603(m) unit circles can be packed is 1 + csc(Pi/k).

Original entry on oeis.org

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

Views

Author

Rick L. Shepherd, Aug 09 2006

Keywords

Comments

From the diagrams in the link it appears likely that 10,12,12 are the next three terms.

Examples

			See A121602 for the case a(8) = 9 pertaining to A121603(8) = 11 unit circles.

Links

Crossrefs

Cf. A121603, A121570, A121598, A121601, A121602.

A384851 Decimal expansion of minimal radius of a circle that contains 14 non-overlapping unit disks.

Original entry on oeis.org

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

Views

Author

Jinyuan Wang, Jun 10 2025

Keywords

Examples

			4.328428554860836681403909367478181...

Links

Crossrefs

Cf. A084618, A121570, A121598, A121601, A121602, A281115, A282279.

Programs

  • PARI
    1+sqrt(1+polrootsreal(Pol([707281, -27270266, 472689975, -4930771548, 34449512067, -168736166642, 591369611109, -1498751280720, 2767422383674, -3746579404052, 3734397946902, -2743990597288, 1486108072662, -593729401364, 175537055738, -38557290064, 6295485573, -759438450, 66647843, -4134492, 172311, -4346, 49]))[10])
Showing 1-4 of 4 results.

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

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