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A246664
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Decimal expansion of 'a', an auxiliary constant associated with the asymptotic probability of success in the secretary problem when the number of applicants is uniformly distributed.
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2
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2, 1, 1, 9, 8, 2, 4, 4, 0, 9, 8, 9, 2, 0, 6, 3, 6, 4, 9, 4, 6, 4, 0, 0, 5, 3, 8, 3, 0, 0, 7, 4, 0, 9, 1, 5, 4, 5, 5, 4, 4, 6, 3, 9, 6, 3, 2, 5, 3, 4, 1, 9, 8, 5, 4, 0, 9, 2, 0, 2, 7, 5, 4, 2, 6, 7, 6, 2, 7, 7, 4, 3, 8, 7, 1, 8, 5, 4, 8, 7, 9, 8, 2, 3, 9, 8, 7, 3, 8, 6, 2, 6, 6, 3, 0, 3, 2, 3, 8, 9
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OFFSET
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1,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361.
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LINKS
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FORMULA
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e^a*(1 - gamma - log(a) + Ei(-a)) - (gamma + log(a) - Ei(a)) = 1, where gamma is Euler's constant and Ei is the exponential integral function.
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EXAMPLE
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2.119824409892063649464005383007409154554463963253419854092...
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MATHEMATICA
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a /. FindRoot[E^a*(1 - EulerGamma - Log[a] + ExpIntegralEi[-a]) - (EulerGamma + Log[a] - ExpIntegralEi[a]) == 1, {a, 2}, WorkingPrecision -> 100] // RealDigits // First
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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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