OFFSET
1,2
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.
FORMULA
log(A242672).
2*Sum_{k >= 3}(log(k)/(k^2-1)) - log(2)/3.
EXAMPLE
1.3531302722959332816529440324922596269...
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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 06 2014
STATUS
approved