A222069 - OEIS

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A222069

Decimal expansion of (1/30)*2^(1/2)*Pi^2.

4, 6, 5, 2, 5, 7, 6, 1, 3, 3, 0, 9, 2, 5, 8, 6, 3, 5, 6, 1, 0, 5, 0, 4, 0, 6, 2, 4, 1, 1, 2, 9, 3, 6, 8, 5, 9, 9, 4, 6, 5, 7, 7, 5, 1, 3, 9, 6, 5, 3, 6, 1, 5, 7, 7, 4, 3, 5, 6, 6, 4, 4, 4, 5, 0, 1, 3, 2, 7, 1, 8, 4, 1, 8, 8, 8, 7, 1, 8, 1, 4, 3, 1, 1, 1, 6, 0, 0, 8, 9, 1, 5, 4, 0, 5, 4

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OFFSET

0,1

COMMENTS

Conjectured to be density of densest packing of equal spheres in five dimensions (achieved for example by the D_5 lattice).

REFERENCES

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

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.7, p. 507.

LINKS

Table of n, a(n) for n=0..95.

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.

G. Nebe and N. J. A. Sloane, Home page for D_5 lattice.

N. J. A. Sloane and Andrey Zabolotskiy, Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space (some values are only conjectural).

Index entries for transcendental numbers.

EXAMPLE

.46525761330925863561050406241129368599465775139653615774...

MATHEMATICA

RealDigits[(Sqrt[2] Pi^2)/30, 10, 120][[1]] (* Harvey P. Dale, Nov 07 2021 *)

PROG

(PARI) Pi^2/sqrt(450) \\ Charles R Greathouse IV, Oct 31 2014