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A374948
Decimal expansion of the Euclidean length of the minimum Steiner tree joining all the vertices of a unit cube.
0
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, 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, 9, 9, 0, 5, 0, 7, 2, 6, 4, 0, 0, 1, 1, 1, 2, 4, 3, 4, 3
OFFSET
1,1
COMMENTS
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).
LINKS
R. Bridges, Minimal Steiner Trees for Three Dimensional Networks, Math. Gaz., 78 (1994), 157-162.
Mathematics Stack Exchange,, Steiner tree problem in 3D.
J. M. Smith, R. Weiss, and M. Patel, An O(N2) Heuristic for Steiner Minimal Trees in E3, Networks 26 (1995), 273-289.
B. Toppur and J. M. A. Smith, A Sausage Heuristic for Steiner Minimal Trees in Three-Dimensional Euclidean Space, J. Math. Modelling and Algorithms, 4 (2005), 199-217.
FORMULA
Equals 3*sqrt(3) + 1.
Equals A010482(n) for any n >= 2 and a(1) = A010482(1) + 1.
EXAMPLE
6.1961524227066318805823390245176171008284157614311418841674209383...
MATHEMATICA
RealDigits[3Sqrt[3]+1, 10, 87][[1]] (* Stefano Spezia, Jul 25 2024 *)
CROSSREFS
Essentially the same as A178809, A176532 and A010482.
Sequence in context: A245724 A021908 A093358 * A155079 A153608 A364618
KEYWORD
nonn,cons
AUTHOR
Marco Ripà, Jul 24 2024
STATUS
approved