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

Author

Jean-François Alcover, Sep 01 2014

Keywords

• nonn
• cons
• easy

Examples

			2.119824409892063649464005383007409154554463963253419854092...
		

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. A246665.

Programs

Mathematica

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

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.