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A246667
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Decimal expansion of 'b', an auxiliary constant associated with the asymptotic probability of success in the full information version of the secretary problem.
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2
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1, 3, 4, 5, 0, 1, 6, 6, 1, 7, 0, 2, 1, 9, 9, 6, 9, 8, 4, 4, 9, 0, 5, 7, 9, 9, 1, 9, 9, 9, 8, 6, 9, 1, 5, 0, 1, 5, 3, 8, 7, 5, 8, 4, 2, 0, 6, 0, 6, 3, 6, 7, 5, 4, 1, 6, 2, 8, 7, 2, 6, 1, 0, 5, 7, 9, 1, 3, 1, 4, 6, 4, 9, 5, 5, 9, 7, 2, 0, 5, 8, 8, 3, 9, 0, 5, 8, 1, 8, 7, 3, 7, 8, 3, 8, 9, 8, 6, 5, 9, 4
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OFFSET
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1,2
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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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Ei(-b) - gamma - log(b) = -1, where gamma is Euler's constant and Ei is the exponential integral function.
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EXAMPLE
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1.3450166170219969844905799199986915015387584206063675416287261...
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MATHEMATICA
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b /. FindRoot[ExpIntegralEi[-b] - EulerGamma - Log[b] == -1, {b, 2}, WorkingPrecision -> 101] // 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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