A246673 Decimal expansion of 'c', an optimal stopping constant associated with the two choice case.

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

Offset

1,3

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

2*xi/(xi + 2), where xi is A246672.

Example

1.165623287731622772082152021107540408255491345963342103019...

Mathematica

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

Crossrefs

Cf. A246672.

Sequence in context: A330065 A191220 A356793 * A220190 A231738 A198829

Adjacent sequences: A246670 A246671 A246672 * A246674 A246675 A246676

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 01 2014

Status

approved