A374948 - OEIS

%I #15 Sep 03 2024 17:55:21

%S 6,1,9,6,1,5,2,4,2,2,7,0,6,6,3,1,8,8,0,5,8,2,3,3,9,0,2,4,5,1,7,6,1,7,

%T 1,0,0,8,2,8,4,1,5,7,6,1,4,3,1,1,4,1,8,8,4,1,6,7,4,2,0,9,3,8,3,5,5,7,

%U 9,9,0,5,0,7,2,6,4,0,0,1,1,1,2,4,3,4,3

%N Decimal expansion of the Euclidean length of the minimum Steiner tree joining all the vertices of a unit cube.

%C The 1994 Bridge's paper entitled "Minimal Steiner Trees for Three Dimensional Networks" (see Links) suggested an optimal strategy to solve the minimum Steiner tree problem for the unit cube {0,1}^3, and the total length of the provided Steiner Tree is 1 + 3*sqrt(3).

%H R. Bridges, <a href="https://www.jstor.org/stable/3618571">Minimal Steiner Trees for Three Dimensional Networks</a>, Math. Gaz., 78 (1994), 157-162.

%H Math Overflow, <a href="https://mathoverflow.net/questions/473016/joining-the-2k-points-of-0-1-k-with-the-shortest-tree">Joining the 2^k points of {0,1}^k with the shortest tree</a>.

%H Mathematics Stack Exchange,, <a href="https://math.stackexchange.com/questions/835759/steiner-tree-problem-in-3d">Steiner tree problem in 3D</a>.

%H J. M. Smith, R. Weiss, and M. Patel, <a href="https://onlinelibrary.wiley.com/doi/abs/10.1002/net.3230260411">An O(N2) Heuristic for Steiner Minimal Trees in E3</a>, Networks 26 (1995), 273-289.

%H B. Toppur and J. M. A. Smith, <a href="https://link.springer.com/article/10.1007/s10852-004-6390-x">A Sausage Heuristic for Steiner Minimal Trees in Three-Dimensional Euclidean Space</a>, J. Math. Modelling and Algorithms, 4 (2005), 199-217.

%F Equals 3*sqrt(3) + 1.

%F Equals A010482(n) for any n >= 2 and a(1) = A010482(1) + 1.

%e 6.1961524227066318805823390245176171008284157614311418841674209383...

%t RealDigits[3Sqrt[3]+1,10,87][[1]] (* _Stefano Spezia_, Jul 25 2024 *)

%Y Cf. A002194, A010482, A374148, A374260.

%Y Essentially the same as A178809, A176532 and A010482.

%K nonn,cons

%O 1,1

%A _Marco Ripà_, Jul 24 2024