%I #19 Feb 07 2025 13:45:53
%S 7,5,4,6,9,7,3,9,9,3,3,7,4,0,5,8,3,0,3,9,1,6,5,2,1,0,5,9,9,0,2,2,9,3,
%T 3,1,3,4,2,4,3,2,1,9,2,1,4,5,9,4,3,4,2,8,4,7,6,5,8,3,5,9,2,0,5,6,1,5,
%U 8,6,6,4,5,0,7,3,0,3,9,0,5,3,0,3,3,2,7,4,6,8
%N Decimal expansion of the upper bound of the density of sphere packing in the Euclidean 3-space resulting from the dodecahedral conjecture.
%C See A374753 for more information on the dodecahedral conjecture.
%H Paolo Xausa, <a href="/A374772/b374772.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LocalDensity.html">Local Density</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F Equals (4/3)*Pi/A374753 = 10*A019699/A374753.
%F Equals A374771/A102769.
%F Equals Pi*sqrt(5 + sqrt(5))/(15*sqrt(10)*(sqrt(5) - 2)).
%F Equals 4*Pi/A374755.
%e 0.7546973993374058303916521059902293313424321921459...
%t First[RealDigits[Pi*Sqrt[5 + Sqrt[5]]/(15*Sqrt[10]*(Sqrt[5] - 2)), 10, 100]]
%o (PARI) Pi*sqrt(5 + sqrt(5))/(15*sqrt(10)*(sqrt(5) - 2)) \\ _Charles R Greathouse IV_, Feb 07 2025
%Y Cf. A374753 (dodecahedral conjecture), A374755 (strong dodecahedral conjecture), A374771, A374837, A374838.
%Y Cf. A093825, A019699, A102769.
%K nonn,cons,changed
%O 0,1
%A _Paolo Xausa_, Jul 19 2024