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, 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

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.

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: A368924 A019803 A214506 * A229962 A141601 A108558

Adjacent sequences: A246661 A246662 A246663 * A246665 A246666 A246667

Keyword

nonn,cons,easy,changed

Author

Jean-François Alcover, Sep 01 2014

Status

approved