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A267040 Decimal expansion of sqrt(8)*arctan(sqrt(2)/5). 3
7, 7, 9, 6, 3, 5, 5, 7, 0, 0, 4, 4, 2, 5, 2, 9, 3, 7, 8, 2, 5, 4, 5, 0, 8, 2, 4, 9, 9, 3, 2, 2, 9, 0, 3, 0, 0, 1, 1, 1, 1, 5, 9, 5, 3, 9, 5, 2, 5, 4, 8, 4, 2, 5, 5, 2, 7, 3, 1, 7, 0, 3, 7, 0, 0, 1, 1, 8, 3, 5, 2, 4, 4, 9, 0, 7, 6, 1, 7, 9, 0, 5, 1, 0, 5, 9, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This constant is the packing density of a regular tetrahedron. That is, let S be a regular tetrahedron of edge length 2 and let B the part of S that lies within distance 1 of some vertex. Then this constant is the ratio of the volume of B to the volume of S.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Thomas C. Hales, A proof of the Kepler conjecture, Annals of Mathematics, Vol. 162, No. 3 (2005), pp. 1065-1185.

Carl A. Rogers, The packing of equal spheres, Proceedings of the London Mathematical Society, Vol. 3, No. 4 (1958), pp. 609-620.

FORMULA

Equals sqrt(8)*arctan(sqrt(2)/5).

Equals 3*A093825 - 2*A266814.

Equals 3*sqrt(2)*(arccos(1/3) - Pi/3). - Amiram Eldar, Jun 26 2021

EXAMPLE

0.77963557004425293782545082499322903001111595395254...

MATHEMATICA

First@ RealDigits@ N[Sqrt[8] ArcTan[Sqrt[2]/5], 120] (* Michael De Vlieger, Jan 09 2016 *)

PROG

(PARI) sqrt(8)*atan(sqrt(2)/5) \\ Michel Marcus, Jan 09 2016

(MAGMA) SetDefaultRealField(RealField(100)); Sqrt(8)*Arctan(Sqrt(2)/5); // G. C. Greubel, Aug 19 2018

CROSSREFS

Cf. A093825, A266814, A267033.

Sequence in context: A021566 A335847 A244649 * A225961 A099290 A224895

Adjacent sequences:  A267037 A267038 A267039 * A267041 A267042 A267043

KEYWORD

nonn,cons

AUTHOR

Martin Renner, Jan 09 2016

STATUS

approved

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Last modified December 1 14:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)