A246672 Decimal expansion of 'xi', an optimal stopping auxiliary constant associated with the two choice case.

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

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..102.

David Assaf, Larry Goldstein, Ester Samuel-Cahn, Two choice optimal stopping.

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 46.

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

Wikipedia, Secretary problem.

Formula

Unique positive solution of (2/xi + 1)*log(xi/2 + 1) = 3/2.

Example

2.79399765260155079609907114136685042580083911662734211613515983...

Mathematica

xi /. FindRoot[(2/xi + 1)*Log[xi/2 + 1] == 3/2, {xi, 3}, WorkingPrecision -> 102] // RealDigits // First

Crossrefs

Cf. A246673.

Sequence in context: A198122 A021362 A371803 * A011054 A276140 A130818

Adjacent sequences: A246669 A246670 A246671 * A246673 A246674 A246675

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 01 2014

Status

approved