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

Author

Jean-François Alcover, Sep 01 2014

Keywords

• nonn
• cons
• easy

Examples

			0.4492472188692162712298793943797092675048587363694594648684...
		

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.
• Eric Weisstein's MathWorld, Sultan's Dowry Problem.
• Wikipedia, Secretary problem.

Crossrefs

Cf. A246667.

Programs

Mathematica

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

Formula

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