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A242461 Decimal expansion of the first positive solution to exp(1-1/x)/x = 1/2, a binary search tree constant. 0
3, 7, 3, 3, 6, 4, 6, 1, 7, 7, 0, 1, 6, 7, 4, 0, 8, 4, 2, 4, 8, 4, 4, 8, 4, 3, 6, 6, 7, 9, 2, 7, 0, 5, 9, 5, 0, 0, 2, 5, 7, 6, 4, 6, 7, 0, 0, 4, 2, 7, 7, 3, 8, 4, 4, 4, 4, 9, 3, 8, 5, 7, 0, 3, 1, 5, 1, 3, 0, 5, 6, 5, 5, 1, 3, 3, 5, 3, 3, 3, 5, 5, 8, 8, 8, 1, 6, 9, 8, 8, 9, 0, 6, 5, 0, 3, 8, 8, 6, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The saturation level S_n of a binary search tree defined by a random n-permutation is such that S_n/log(n) converges to 0.3733646... in probability.

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 349-352.

LINKS

Table of n, a(n) for n=0..99.

Luc Devroye, A Note on the Height of Binary Search Trees. McGill University, Montreal, Canada (1986).

FORMULA

-1/W(-1, -1/(2*e)) where W is the Lambert W function (ProductLog).

EXAMPLE

0.373364617701674084248448436679270595...

MATHEMATICA

RealDigits[-1/ProductLog[-1, -1/(2*E)], 10, 100] // First

CROSSREFS

Cf. A076615, A076616, A195581, A195582, A195596.

Sequence in context: A283245 A066065 A145511 * A065443 A198350 A117190

Adjacent sequences:  A242458 A242459 A242460 * A242462 A242463 A242464

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, May 15 2014

STATUS

approved

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Last modified July 24 01:41 EDT 2021. Contains 346269 sequences. (Running on oeis4.)