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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
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
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
KEYWORD
nonn,cons
AUTHOR
STATUS
approved