A242672 Decimal expansion of an optimal stopping constant related to the Secretary problem.

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

Offset: 1

Author

Jean-François Alcover, May 20 2014

Keywords

• nonn
• cons

Examples

			3.869519241397999495694167278779...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15, p. 362.

Links

• Eric Weisstein's MathWorld, Sultan's Dowry Problem.
• Wikipedia, Secretary problem.

Crossrefs

Cf. A054404, A242673, A242674.

Programs

Mathematica

NProduct[(1+2/k)^(1/(k+1)), {k, 1, Infinity}, NProductFactors -> 1000, WorkingPrecision -> 48] // RealDigits[#, 10, 40]& // First

Formula

product_(k>0) (1+2/k)^(1/(k+1)).

Also equals exp(2*Sum_{k>=3} (log(k)/(k^2-1)) - log(2)/3).

Extensions

More terms from Alois P. Heinz, Jun 06 2014