

A222072


Decimal expansion of (1/384)*Pi^4.


12



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

0,1


COMMENTS

Conjectured to be density of densest packing of equal spheres in 8 dimensions (achieved for example by the D_8 lattice).
The above conjecture is true (cf. Viazovska, 2017).  Felix FrÃ¶hlich, Jan 08 2018


REFERENCES

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


LINKS

Table of n, a(n) for n=0..101.
J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete & Computational Geometry, Vol. 13, No. 34 (1995), 383403.
G. Nebe and N. J. A. Sloane, Home page for E_8 lattice
N. J. A. Sloane, Table of maximal density of a packing of equal spheres in ndimensional Euclidean space (for n>3 the values are only conjectural).
M. S. Viazovska, The sphere packing problem in dimension 8, Annals of Mathematics, Vol. 185, No. 3 (2017), 9911015.
M. S. Viazovska, The sphere packing problem in dimension 8, arXiv:1603.04246 [math.NT], 2017.


FORMULA

Equals Sum_{n>=1} Sum_{k>=n} 1/(2*n  1)^2/(2*k + 1)^2.  Geoffrey Critzer, Nov 03 2013


EXAMPLE

.25366950790104801363656336637683622721283225435595161898819...


MATHEMATICA

RealDigits[Pi^4/ 384, 10, 120][[1]] (* Harvey P. Dale, Aug 11 2015 *)


PROG

(PARI) Pi^4/384 \\ Charles R Greathouse IV, Oct 31 2014


CROSSREFS

Related constants: A020769, A020789, A093766, A093825, A222066, A222067, A222068, A222069, A222070, A222071, A222073, A222074, A222075.
Sequence in context: A160516 A264105 A024871 * A246007 A256997 A239970
Adjacent sequences: A222069 A222070 A222071 * A222073 A222074 A222075


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane, Feb 10 2013


STATUS

approved



