A246671 Decimal expansion of Shepp's constant 'alpha', an optimal stopping constant associated with the case of a zero mean and unit variance distribution function.

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

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..102.

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 45.

L. A. Shepp, Explicit Solutions to Some Problems of Optimal Stopping.

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

Wikipedia, Secretary problem.

Formula

Unique zero of 2*x - sqrt(2*Pi)*(1 - x^2)*exp(x^2/2)*(1 + erf(x/sqrt(2))).

Example

0.83992367569237268960377697742181556936162069870391285...

Mathematica

x /. FindRoot[2*x - Sqrt[2*Pi]*(1 - x^2)*Exp[x^2/2]*(1 + Erf[x/Sqrt[2]]) == 0, {x, 1}, WorkingPrecision -> 103] // RealDigits // First

Crossrefs

Cf. A246664, A246665, A246667, A246668.

Sequence in context: A090734 A200614 A011467 * A069610 A257811 A122159

Adjacent sequences: A246668 A246669 A246670 * A246672 A246673 A246674

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 01 2014

Status

approved