A246668 Decimal expansion of the asymptotic probability of success in the full information version of the secretary problem.

4, 4, 9, 2, 4, 7, 2, 1, 8, 8, 6, 9, 2, 1, 6, 2, 7, 1, 2, 2, 9, 8, 7, 9, 3, 9, 4, 3, 7, 9, 7, 0, 9, 2, 6, 7, 5, 0, 4, 8, 5, 8, 7, 3, 6, 3, 6, 9, 4, 5, 9, 4, 6, 4, 8, 6, 8, 4, 1, 3, 7, 4, 7, 6, 4, 4, 9, 3, 5, 5, 5, 8, 6, 7, 2, 6, 3, 2, 6, 4, 2, 4, 5, 5, 4, 8, 0, 4, 3, 7, 2, 7, 6, 8, 7, 6, 8, 4, 1, 5, 1

Offset

0,1

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=0..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^(-b) - (e^b - b - 1)*Ei(-b), where b is A246667 and Ei is the exponential integral function.

Example

0.4492472188692162712298793943797092675048587363694594648684...

Mathematica

b = x /. FindRoot[ExpIntegralEi[-x] - EulerGamma - Log[x] == -1, {x, 2}, WorkingPrecision -> 102]; E^-b - (E^b - b - 1)*ExpIntegralEi[-b] // RealDigits // First

Crossrefs

Cf. A246667.

Sequence in context: A165441 A204997 A178840 * A021073 A021961 A115365

Adjacent sequences: A246665 A246666 A246667 * A246669 A246670 A246671

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 01 2014

Status

approved