A243533 Decimal expansion of 'c', an asymptotic constant related to a variation of the "Secretary problem" with a uniform distribution.

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

Offset: 1

Author

Jean-François Alcover, Jun 06 2014

Keywords

• nonn
• cons

Examples

			1.3531302722959332816529440324922596269...
		

References

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

Links

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

Crossrefs

Cf. A054404, A242672.

Programs

Mathematica

digits = 65; c = 2*NSum[Log[k]/(k^2 - 1), {k, 3, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 10^4, Method -> {"EulerMaclaurin", Method -> {"NIntegrate", "MaxRecursion" -> 10, Method -> "DoubleExponential"}}] - (Log[2]/3); RealDigits[c, 10, digits] // First

Formula

log(A242672).

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