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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 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-François 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.)