A246667 Decimal expansion of 'b', an auxiliary constant associated with the asymptotic probability of success in the full information version of the secretary problem.

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

Offset

1,2

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..101.

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

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

Wikipedia, Secretary problem.

Formula

Ei(-b) - gamma - log(b) = -1, where gamma is Euler's constant and Ei is the exponential integral function.

Example

1.3450166170219969844905799199986915015387584206063675416287261...

Mathematica

b /. FindRoot[ExpIntegralEi[-b] - EulerGamma - Log[b] == -1, {b, 2}, WorkingPrecision -> 101] // RealDigits // First

Crossrefs

Cf. A246668.

Sequence in context: A158962 A263824 A215747 * A199066 A306584 A176948

Adjacent sequences: A246664 A246665 A246666 * A246668 A246669 A246670

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 01 2014

Status

approved