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A019673 Decimal expansion of Pi/6. 16
5, 2, 3, 5, 9, 8, 7, 7, 5, 5, 9, 8, 2, 9, 8, 8, 7, 3, 0, 7, 7, 1, 0, 7, 2, 3, 0, 5, 4, 6, 5, 8, 3, 8, 1, 4, 0, 3, 2, 8, 6, 1, 5, 6, 6, 5, 6, 2, 5, 1, 7, 6, 3, 6, 8, 2, 9, 1, 5, 7, 4, 3, 2, 0, 5, 1, 3, 0, 2, 7, 3, 4, 3, 8, 1, 0, 3, 4, 8, 3, 3, 1, 0, 4, 6, 7, 2, 4, 7, 0, 8, 9, 0, 3, 5, 2, 8, 4, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From Omar E. Pol, Aug 30 2007: (Start)

Pi/6 = Volume of the inscribed ellipsoid / (Volume of the cuboid (If L1>L2>L3)).

Pi/6 = Volume of the inscribed spheroid / (Volume of the cuboid (If L1>(L2=L3))).

Pi/6 = Volume of the inscribed spheroid / (Volume of the cuboid (If L1<(L2=L3))).

Pi/6 = Volume of the inscribed sphere / (Volume of the regular hexahedron (Or cube)).  (End)

Pi/6 = Surface area of the inscribed sphere / (surface area of the regular hexahedron (or cube)). - Omar E. Pol, Nov 13 2007

Decimal expansion of arctan(sqrt(1/3)). - Clark Kimberling, Sep 23 2011

Also, decimal expansion of sum( k>=1, (-120+329*k+568*k^2)/(k*(1+k)*(1+2*k)*(1+4*k)*(3+4*k)*(5+4*k)) ). [Bruno Berselli, Dec 01 2013]

Atomic packing factor (APF) of the simple cubic lattice filled with spheres of the same diameter (unique example among chemical elements: polonium crystal). - Stanislav Sykora, Sep 29 2014

REFERENCES

Ian Stewart, Professor Stewart's Cabinet of Mathematical Curiosities, Basic Books, a member of the Perseus Books Group, NY, 2009, "A Constant Bore", pp. 49-50 & 264-266.

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Wikipedia, Atomic packing factor

EXAMPLE

Pi/6 = 0.5235987755982988730771072305465838140328615665625176368291574...

MATHEMATICA

RealDigits[N[Pi/6, 6! ]] (* Vladimir Joseph Stephan Orlovsky, Dec 02 2009 *)

PROG

(PARI) Pi/6 \\ Charles R Greathouse IV, Jul 07 2014

CROSSREFS

Cf. A000796, A132696.

Cf. APF's of other crystal lattices: A093825 (hcp,fcc), A247446 (diamond cubic).

Sequence in context: A097078 A237200 A021195 * A229780 A272031 A090183

Adjacent sequences:  A019670 A019671 A019672 * A019674 A019675 A019676

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 27 02:08 EDT 2017. Contains 284143 sequences.