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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 = 0..20000
James Grime and Brady Haran, The Best Way to Pack Spheres, Numberphile video (2018).
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, Cubic Close Packing
Eric Weisstein's World of Mathematics, Ellipsoid Packing
Eric Weisstein's World of Mathematics, Sphere 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: A303982 A175998 A306398 * 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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