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A093825
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Decimal expansion of Pi/(3*sqrt(2)).
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20
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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
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OFFSET
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0,1
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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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
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FORMULA
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Equals A019670*A010503. - R. J. Mathar, Feb 05 2009
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EXAMPLE
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0.74048048969306104116931349834344894976910361489594837...
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MATHEMATICA
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RealDigits[Pi/(3*Sqrt[2]), 10, 120][[1]] (* Harvey P. Dale, Feb 03 2012 *)
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PROG
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(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
(PARI) Pi/sqrt(18) \\ Charles R Greathouse IV, May 11 2017
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CROSSREFS
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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
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Eric W. Weisstein, Apr 16 2004
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EXTENSIONS
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Entry revised by N. J. A. Sloane, Feb 10 2013
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STATUS
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approved
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