cp's OEIS Frontend

A374772 Decimal expansion of the upper bound of the density of sphere packing in the Euclidean 3-space resulting from the dodecahedral conjecture.

%I A374772 #26 May 21 2025 01:34:39
%S A374772 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 A374772 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 A374772 8,6,6,4,5,0,7,3,0,3,9,0,5,3,0,3,3,2,7,4,6,8
%N A374772 Decimal expansion of the upper bound of the density of sphere packing in the Euclidean 3-space resulting from the dodecahedral conjecture.
%C A374772 See A374753 for more information on the dodecahedral conjecture.
%C A374772 Also isoperimetric quotient (see A381671 for definition) of a regular dodecahedron. - _Paolo Xausa_, May 19 2025
%H A374772 Paolo Xausa, <a href="/A374772/b374772.txt">Table of n, a(n) for n = 0..10000</a>
%H A374772 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LocalDensity.html">Local Density</a>.
%H A374772 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A374772 Equals (4/3)*Pi/A374753 = 10*A019699/A374753.
%F A374772 Equals A374771/A102769.
%F A374772 Equals Pi*sqrt(5 + sqrt(5))/(15*sqrt(10)*(sqrt(5) - 2)).
%F A374772 Equals 4*Pi/A374755.
%F A374772 Equals 36*Pi*A102769^2/(A131595^3). - _Paolo Xausa_, May 19 2025
%e A374772 0.7546973993374058303916521059902293313424321921459...
%t A374772 First[RealDigits[Pi*Sqrt[5 + Sqrt[5]]/(15*Sqrt[10]*(Sqrt[5] - 2)), 10, 100]]
%o A374772 (PARI) Pi*sqrt(5 + sqrt(5))/(15*sqrt(10)*(sqrt(5) - 2)) \\ _Charles R Greathouse IV_, Feb 07 2025
%Y A374772 Cf. A374753 (dodecahedral conjecture), A374755 (strong dodecahedral conjecture), A374771, A374837, A374838.
%Y A374772 Cf. A093825, A019699, A102769, A131595, A381671.
%K A374772 nonn,cons
%O A374772 0,1
%A A374772 _Paolo Xausa_, Jul 19 2024