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A222070 Decimal expansion of (1/144)*3^(1/2)*Pi^3.

%I A222070 #23 Dec 24 2024 09:38:28
%S A222070 3,7,2,9,4,7,5,4,5,5,8,2,0,6,4,9,3,9,5,6,3,4,7,7,5,5,8,6,7,9,9,5,8,1,
%T A222070 0,6,3,9,3,6,6,4,7,9,7,2,6,8,3,8,7,3,6,3,1,1,1,4,0,4,0,6,5,5,9,7,2,8,
%U A222070 3,1,7,2,0,2,9,6,8,3,2,1,9,5,2,2,5,2,6,7,2,1,6,3,5,3,4,0,5,4,2,7,6
%N A222070 Decimal expansion of (1/144)*3^(1/2)*Pi^3.
%C A222070 Conjectured to be density of densest packing of equal spheres in six dimensions (achieved for example by the E_6 lattice).
%D A222070 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. xix.
%D A222070 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.7, p. 507.
%H A222070 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 A222070 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/E6.html">Home page for E_6 lattice</a>.
%H A222070 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 A222070 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A222070 0.3729475455820649395634775586799581063936647972683873631...
%t A222070 RealDigits[Sqrt[3]*Pi^3/144, 10, 120][[1]] (* _Amiram Eldar_, Jun 28 2023 *)
%o A222070 (PARI) Pi^3*sqrt(3)/144 \\ _Charles R Greathouse IV_, Oct 31 2014
%Y A222070 Related constants: A020769, A020789, A093766, A093825, A222066, A222067, A222068, A222069, A222071, A222072, A260646.
%K A222070 nonn,cons
%O A222070 0,1
%A A222070 _N. J. A. Sloane_, Feb 10 2013