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A195600 Continued fraction for beta = 3/(2*log(alpha/2)); alpha = A195596. 6
1, 1, 20, 3, 2, 7, 1, 1, 1, 12, 1, 5, 1, 91, 1, 1, 3, 87, 2, 1, 1, 1, 1, 3, 1, 9, 3, 2, 1, 1, 1, 1, 190, 1, 3, 1, 82, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 2, 12, 6, 2, 2, 2, 3, 2, 1, 1, 1, 2, 3, 21, 1, 1, 12, 1, 7, 3, 2, 26, 3, 2, 1, 1, 1, 9, 1, 15, 4, 3, 3, 1, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..83.

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

FORMULA

beta = 3/(2*log(alpha/2)) = 3*alpha/(2*alpha-2), where alpha = A195596 = -1/W(-exp(-1)/2) and W is the Lambert W function.

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

EXAMPLE

1.95302570335815413945406288542575380414251340201036319609354...

MAPLE

with(numtheory):

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

beta:= 3/(2*log(alpha/2)):

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

MATHEMATICA

beta = 3/(2+2*ProductLog[-1/(2*E)]); ContinuedFraction[beta, 83] (* Jean-Fran├žois Alcover, Jun 20 2013 *)

CROSSREFS

Cf. A195599 (decimal expansion), A195601 (Engel expansion), A195581, A195582, A195583, A195596, A195597, A195598.

Sequence in context: A040390 A040391 A255860 * A118295 A070645 A248136

Adjacent sequences:  A195597 A195598 A195599 * A195601 A195602 A195603

KEYWORD

nonn,cofr

AUTHOR

Alois P. Heinz, Sep 21 2011

STATUS

approved

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)