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A093825 Decimal expansion of Pi/(3*sqrt(2)). 20
7, 4, 0, 4, 8, 0, 4, 8, 9, 6, 9, 3, 0, 6, 1, 0, 4, 1, 1, 6, 9, 3, 1, 3, 4, 9, 8, 3, 4, 3, 4, 4, 8, 9, 4, 9, 7, 6, 9, 1, 0, 3, 6, 1, 4, 8, 9, 5, 9, 4, 8, 3, 7, 0, 5, 1, 4, 2, 3, 2, 6, 0, 1, 1, 5, 9, 4, 0, 5, 7, 9, 8, 8, 4, 9, 9, 1, 2, 3, 1, 8, 4, 2, 9, 2, 2, 1, 1, 5, 5, 7, 9, 4, 1, 2, 7, 5, 3, 9, 5, 6, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Density of densest packing of equal spheres in three dimensions (achieved for example by the fcc lattice).

Atomic packing factor (APF) of the face-centered-cubic (fcc) and the hexagonal-close-packed (hcp) crystal lattices filled with spheres of the same diameter. - Stanislav Sykora, Sep 29 2014

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. xix.

Clifford A. Pickover, The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (2009), at 126.

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000

J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discr. Comp. Geom., 13 (1995), 383-403.

T. C. Hales, Home Page (see under Dense Sphere Packings

G. Nebe and N. J. A. Sloane, Home page for fcc lattice

N. J. A. Sloane, Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space (for n>3 the values are only conjectural).

Eric Weisstein's World of Mathematics, Sphere Packing

Eric Weisstein's World of Mathematics, Ellipsoid Packing

Wikipedia, Atomic packing factor

FORMULA

Equals A019670*A010503. - R. J. Mathar, Feb 05 2009

EXAMPLE

0.74048048969306104116931349834344894976910361489594837...

MATHEMATICA

RealDigits[Pi/(3*Sqrt[2]), 10, 120][[1]] (* Harvey P. Dale, Feb 03 2012 *)

PROG

(PARI) { default(realprecision, 20080); x=10*Pi*sqrt(2)/6; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b093825.txt", n, " ", d)); } \\ Harry J. Smith, Jun 18 2009

CROSSREFS

Cf. A093824.

Cf. APF's of other crystal lattices: A019673 (simple cubic), A247446 (diamond cubic).

Cf. A161686 Continued fraction. - Harry J. Smith, Jun 18 2009

Related constants: A020769, A020789, A093766, A222066, A222067, A222068, A222069, A222070, A222071, A222072, A222073, A222074, A222075.

Sequence in context: A110792 A221388 A175998 * A229784 A091494 A021139

Adjacent sequences:  A093822 A093823 A093824 * A093826 A093827 A093828

KEYWORD

nonn,cons,easy

AUTHOR

Eric W. Weisstein, Apr 16 2004

EXTENSIONS

Entry revised by N. J. A. Sloane, Feb 10 2013

STATUS

approved

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Last modified March 22 22:17 EDT 2017. Contains 283901 sequences.