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 A246665 Decimal expansion of the asymptotic probability of success in the full-information secretary problem with uniform distribution when the number of applicants is also uniformly distributed. 4
 4, 3, 5, 1, 7, 0, 8, 0, 5, 5, 8, 0, 1, 2, 7, 6, 5, 8, 0, 5, 9, 1, 8, 9, 9, 1, 2, 8, 4, 7, 8, 5, 8, 4, 1, 0, 4, 2, 7, 9, 6, 2, 5, 9, 4, 7, 5, 3, 4, 7, 0, 2, 4, 7, 0, 2, 9, 7, 9, 1, 2, 3, 0, 4, 4, 3, 9, 0, 6, 6, 5, 8, 7, 5, 4, 4, 3, 0, 3, 3, 5, 7, 8, 4, 9, 9, 7, 6, 6, 2, 8, 6, 8, 5, 0, 2, 6, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS In this variant of the secretary problem, the applicants' values are independently distributed on a known interval, like in A242674; and the number of applicants is itself a random variable with uniform distribution on 1..n (and then the limit n -> is taken), like in A325905. So we have more information than in the variant considered in A325905 but less information then in the variant considered in A242674. Hence A325905 < this constant < A242674. - Andrey Zabolotskiy, Sep 14 2019 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361. LINKS Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 45. Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author] Zdzisław Porosiński, On best choice problems having similar solutions, Statistics & Probability Letters, 56 (2002), 321-327. Eric Weisstein's MathWorld, Sultan's Dowry Problem Wikipedia, Secretary problem FORMULA (1 - e^a)*Ei(-a) - (e^(-a) + a*Ei(-a))*(gamma + log(a) - Ei(a)), where a is A246664, gamma is Euler's constant and Ei is the exponential integral function. EXAMPLE 0.43517080558012765805918991284785841042796259475347024702979123... MATHEMATICA a = x /. FindRoot[E^x*(1 - EulerGamma - Log[x] + ExpIntegralEi[-x]) - (EulerGamma + Log[x] - ExpIntegralEi[x]) == 1, {x, 2}, WorkingPrecision -> 102]; (1 - E^a)*ExpIntegralEi[-a] - (E^-a + a*ExpIntegralEi[-a])*(EulerGamma + Log[a] - ExpIntegralEi[a]) // RealDigits // First CROSSREFS Cf. A246664, A068985, A325905, A242674. Sequence in context: A292612 A316254 A029934 * A274260 A011397 A081665 Adjacent sequences:  A246662 A246663 A246664 * A246666 A246667 A246668 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Sep 01 2014 STATUS approved

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Last modified October 21 17:26 EDT 2019. Contains 328303 sequences. (Running on oeis4.)