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A260646 Decimal expansion of Pi^12/12!, the absolute density of the Leech lattice.

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%I A260646 #29 Dec 30 2023 08:13:50
%S A260646 0,0,1,9,2,9,5,7,4,3,0,9,4,0,3,9,2,3,0,4,7,9,0,3,3,4,5,5,6,3,6,8,5,9,
%T A260646 5,7,6,4,0,1,6,8,4,7,1,8,1,5,0,0,0,3,0,3,3,5,2,2,3,4,6,4,7,6,1,7,3,3,
%U A260646 1,4,9,5,6,3,4,2,5,0,9,8,5,5,3,1,4,8,7
%N A260646 Decimal expansion of Pi^12/12!, the absolute density of the Leech lattice.
%H A260646 Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko and Maryna Viazovska, <a href="https://doi.org/10.4007/annals.2017.185.3.8">The sphere packing problem in dimension 24</a>, Annals of Mathematics, 185 (2017), 1017-1033; arXiv:<a href="https://arxiv.org/abs/1603.06518">1603.06518</a> [math.NT], 2016-2017.
%H A260646 J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1007/978-1-4757-2016-7">Sphere Packings, Lattices and Groups</a>, Springer-Verlag, 1998 (see also <a href="http://neilsloane.com/doc/splag.html#:~:text=Corrections%20and%20Updates">Corrections and Updates</a>), Chapter 4, Section 11.
%H A260646 G. Nebe and N. J. A. Sloane, <a href="https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/Leech.html">Home page for Leech lattice</a>.
%H A260646 A. Roberts, <a href="http://math.ups.edu/~bryans/Current/Journal_Spring_2006/ARoberts_LeechLattice.pdf">Properties of the Leech Lattice</a>, 2006.
%H A260646 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 A260646 Wikipedia, <a href="https://en.wikipedia.org/wiki/Leech_lattice">Leech lattice</a>
%H A260646 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A260646 0.001929574309403923047903345563685957640168471815...
%t A260646 RealDigits[N[Pi^12/12!, 120]]//First (* _Michael De Vlieger_, Nov 12 2015 *)
%o A260646 (PARI) { default(realprecision, 50080); x=Pi^12/12!; for(n=1, 100, d=floor(x); x=(x-d)*10; print1(d, ", ")) }
%Y A260646 Densities of other lattices: A093766, A093825, A222068, A222069, A222070, A222071, A222072.
%Y A260646 Related to Leech lattice: A008408, A323282.
%K A260646 nonn,cons
%O A260646 0,4
%A A260646 _Felix Fröhlich_, Nov 12 2015