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%I #28 Mar 26 2023 10:27:02
%S 5,2,6,5,5,3,6,7,2,3,1,6,3,8,4,1,8,0,7,9,0,9,6,0,4,5,1,9,7,7,4,0,1,1,
%T 2,9,9,4,3,5,0,2,8,2,4,8,5,8,7,5,7,0,6,2,1,4,6,8,9,2,6,5,5,3,6,7,2,3,
%U 1,6,3,8,4,1,8,0,7,9,0,9,6,0,4,5,1,9
%N Decimal expansion of 466/885.
%C This is the average length of a shortest path between two random points on the infinite Sierpinski gasket of unit side.
%C 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.
%H Burkard Polster, <a href="https://www.youtube.com/watch?v=MbonokcLbNo">The ultimate algorithm</a>, Mathologer video (2021)
%H T. Chan, <a href="http://dx.doi.org/10.1080/00207168908803728">A statistical analysis of the Towers of Hanoi problem</a>, International Journal of Computer Mathematics 28 (1988), 543-623.
%H A. Hinz, <a href="https://dx.doi.org/10.5169/seals-57378">The Tower of Hanoi</a>, L'Enseignement mathématique 35 (1989), 289-321.
%H A. Hinz, <a href="http://dx.doi.org/10.1016/0020-0255(92)90067-I">Shortest paths between regular states of the Tower of Hanoi</a>, Information Sciences 63 (1992), 173-181.
%H A. Hinz and A. Schief, <a href="http://dx.doi.org/10.1007/BF01217750">The average distance on the Sierpinski gasket</a>, Probability Theory and Related Fields 87 (1990), 129-138.
%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%e 466/885 = 0.5265536723... is a repeating decimal with nonperiod length 1 and period length 58.
%e 466/885 = 0.5(2655367231638418079096045197740112994350282485875706214689). - _Andrey Zabolotskiy_, Sep 07 2016
%t First@ RealDigits@ N[466/885, 120] (* _Michael De Vlieger_, Sep 07 2016 *)
%K nonn,cons,easy
%O 0,1
%A _Martin Renner_, Sep 06 2016
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