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A222069 Decimal expansion of (1/30)*2^(1/2)*Pi^2.

%I A222069 #21 Dec 24 2024 09:38:23
%S A222069 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,
%T A222069 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,
%U A222069 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
%N A222069 Decimal expansion of (1/30)*2^(1/2)*Pi^2.
%C A222069 Conjectured to be density of densest packing of equal spheres in five dimensions (achieved for example by the D_5 lattice).
%D A222069 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. xix.
%D A222069 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.7, p. 507.
%H A222069 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 A222069 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/D5.html">Home page for D_5 lattice</a>.
%H A222069 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 A222069 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A222069 .46525761330925863561050406241129368599465775139653615774...
%t A222069 RealDigits[(Sqrt[2] Pi^2)/30,10,120][[1]] (* _Harvey P. Dale_, Nov 07 2021 *)
%o A222069 (PARI) Pi^2/sqrt(450) \\ _Charles R Greathouse IV_, Oct 31 2014
%Y A222069 Related constants: A020769, A020789, A093766, A093825, A222066, A222067, A222068, A222070, A222071, A222072, A260646.
%K A222069 nonn,cons
%O A222069 0,1
%A A222069 _N. J. A. Sloane_, Feb 10 2013