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A195596
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Decimal expansion of alpha, the unique solution on [2,oo) of the equation alpha*log((2*e)/alpha)=1.
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9
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4, 3, 1, 1, 0, 7, 0, 4, 0, 7, 0, 0, 1, 0, 0, 5, 0, 3, 5, 0, 4, 7, 0, 7, 6, 0, 9, 6, 4, 4, 6, 8, 9, 0, 2, 7, 8, 3, 9, 1, 5, 6, 2, 9, 9, 8, 0, 4, 0, 2, 8, 8, 0, 5, 0, 6, 6, 9, 3, 7, 8, 8, 4, 4, 4, 6, 2, 4, 8, 2, 9, 5, 7, 4, 9, 5, 1, 4, 1, 6, 6, 4, 6, 0, 1, 4, 9, 5, 6, 4, 3, 9, 4, 4, 1, 4, 4, 9, 0, 9, 6, 6, 9, 0, 1
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OFFSET
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1,1
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COMMENTS
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alpha is used to measure the expected height of random binary search trees.
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.13 Binary search tree constants, p. 352.
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LINKS
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Larry Shepp, Doron Zeilberger and Cun-Hui Zhang, Pick up sticks, arXiv preprint arXiv:1210.5642 [math.CO] (2012).
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FORMULA
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alpha = -1/W(-exp(-1)/2), where W is the Lambert W function.
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EXAMPLE
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4.31107040700100503504707609644689027839156299804028805066937...
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MAPLE
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alpha:= solve(alpha*log((2*exp(1))/alpha)=1, alpha):
as:= convert(evalf(alpha/10, 130), string):
seq(parse(as[n+1]), n=1..120);
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MATHEMATICA
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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