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A246664 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. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361.

LINKS

Table of n, a(n) for n=1..100.

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]

Eric Weisstein's MathWorld, Sultan's Dowry Problem.

Wikipedia, Secretary problem.

FORMULA

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.

EXAMPLE

2.119824409892063649464005383007409154554463963253419854092...

MATHEMATICA

a /. FindRoot[E^a*(1 - EulerGamma - Log[a] + ExpIntegralEi[-a]) - (EulerGamma + Log[a] - ExpIntegralEi[a]) == 1, {a, 2}, WorkingPrecision -> 100] // RealDigits // First

CROSSREFS

Cf. A246665.

Sequence in context: A156883 A019803 A214506 * A229962 A141601 A108558

Adjacent sequences:  A246661 A246662 A246663 * A246665 A246666 A246667

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Sep 01 2014

STATUS

approved

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Last modified October 16 16:16 EDT 2019. Contains 328101 sequences. (Running on oeis4.)