OFFSET
0,1
COMMENTS
This is the average length of a shortest path between two random points on the infinite Sierpinski gasket of unit side.
The average number of moves in a shortest path between two random configurations in the n-disk Tower of Hanoi is asymptotically (1 + o(1))*466/885*2^n.
LINKS
Burkard Polster, The ultimate algorithm, Mathologer video (2021)
T. Chan, A statistical analysis of the Towers of Hanoi problem, International Journal of Computer Mathematics 28 (1988), 543-623.
A. Hinz, The Tower of Hanoi, L'Enseignement mathématique 35 (1989), 289-321.
A. Hinz, Shortest paths between regular states of the Tower of Hanoi, Information Sciences 63 (1992), 173-181.
A. Hinz and A. Schief, The average distance on the Sierpinski gasket, Probability Theory and Related Fields 87 (1990), 129-138.
EXAMPLE
466/885 = 0.5265536723... is a repeating decimal with nonperiod length 1 and period length 58.
466/885 = 0.5(2655367231638418079096045197740112994350282485875706214689). - Andrey Zabolotskiy, Sep 07 2016
MATHEMATICA
First@ RealDigits@ N[466/885, 120] (* Michael De Vlieger, Sep 07 2016 *)
CROSSREFS
KEYWORD
AUTHOR
Martin Renner, Sep 06 2016
STATUS
approved