A222071 - OEIS

%I #20 Dec 30 2023 09:51:22

%S 2,9,5,2,9,7,8,7,3,1,4,5,7,1,2,5,7,3,0,9,9,7,7,4,4,2,9,2,1,0,4,8,9,4,

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

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

%N Decimal expansion of (1/105)*Pi^3.

%C Conjectured to be density of densest packing of equal spheres in 7 dimensions (achieved for example by the E_7 lattice).

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

%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1007/BF02574051">What are all the best sphere packings in low dimensions?</a>, Discr. Comp. Geom., 13 (1995), 383-403.

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/E7.html">Home page for E_7 lattice</a>.

%H N. J. A. Sloane and Andrey Zabolotskiy, <a href="/A093825/a093825_1.txt">Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space (some values are only conjectural)</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e 0.295297873145712573099774429210489478116431319675...

%t RealDigits[Pi^3/105, 10, 120][[1]] (* _Amiram Eldar_, Jun 28 2023 *)

%o (PARI) Pi^3/105 \\ _Charles R Greathouse IV_, Oct 31 2014

%Y Related constants: A020769, A020789, A093766, A093825, A222066, A222067, A222068, A222069, A222070, A222072, A260646.

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_, Feb 10 2013