A276566 Decimal expansion of 466/885.

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, 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, 1, 6, 3, 8, 4, 1, 8, 0, 7, 9, 0, 9, 6, 0, 4, 5, 1, 9

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

Table of n, a(n) for n=0..85.

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.

Index entries for sequences related to Towers of Hanoi

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

Sequence in context: A232356 A211015 A077141 * A158624 A363238 A021659

Adjacent sequences: A276563 A276564 A276565 * A276567 A276568 A276569

Keyword

nonn,cons,easy

Author

Martin Renner, Sep 06 2016

Status

approved