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A195597 Continued fraction for alpha, the unique solution on [2,oo) of the equation alpha*log((2*e)/alpha)=1. 6
4, 3, 4, 1, 1, 1, 11, 2, 19, 1, 3, 1, 1, 1, 14, 1, 3, 5, 58, 3, 1, 10, 1, 1, 6, 5, 13, 127, 1, 1, 7, 13, 1, 2, 1, 2, 2, 1, 2, 2, 4, 2, 4, 1, 1, 6, 9, 3, 1, 16, 1, 3, 2, 32, 3, 1, 1, 2, 11, 1, 13, 4, 2, 1, 1, 1, 1, 2, 2, 6, 1, 1, 1, 2, 25, 1, 5, 5, 1, 1, 1, 1, 5, 2, 3, 2, 5, 25, 1, 190, 2, 1, 5, 3, 1, 20, 1, 1, 2, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

alpha is used to measure the expected height of random binary search trees.

LINKS

Table of n, a(n) for n=1..101.

B. Reed, The height of a random binary search tree, J. ACM, 50 (2003), 306-332.

FORMULA

alpha = -1/W(-exp(-1)/2), where W is the Lambert W function.

A195582(n)/A195583(n) = alpha*log(n) - beta*log(log(n)) + O(1), with beta = 1.953... (A195599).

EXAMPLE

4.31107040700100503504707609644689027839156299804028805066937...

MAPLE

with(numtheory):

alpha:= solve(alpha*log((2*exp(1))/alpha)=1, alpha):

cfrac(evalf(alpha, 130), 100, 'quotients')[];

MATHEMATICA

alpha = -1/ProductLog[-1/(2*E)]; ContinuedFraction[alpha, 101] (* Jean-Fran├žois Alcover, Jun 20 2013 *)

CROSSREFS

Cf. A195596 (decimal expansion), A195598 (Engel expansion), A195581, A195582, A195583, A195599, A195600, A195601.

Sequence in context: A070431 A070511 A066340 * A143505 A245727 A280822

Adjacent sequences:  A195594 A195595 A195596 * A195598 A195599 A195600

KEYWORD

nonn,cofr

AUTHOR

Alois P. Heinz, Sep 21 2011

STATUS

approved

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)