login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A246665 Decimal expansion of the asymptotic probability of success in the full-information secretary problem with uniform distribution when the number of applicants is also uniformly distributed. 4
4, 3, 5, 1, 7, 0, 8, 0, 5, 5, 8, 0, 1, 2, 7, 6, 5, 8, 0, 5, 9, 1, 8, 9, 9, 1, 2, 8, 4, 7, 8, 5, 8, 4, 1, 0, 4, 2, 7, 9, 6, 2, 5, 9, 4, 7, 5, 3, 4, 7, 0, 2, 4, 7, 0, 2, 9, 7, 9, 1, 2, 3, 0, 4, 4, 3, 9, 0, 6, 6, 5, 8, 7, 5, 4, 4, 3, 0, 3, 3, 5, 7, 8, 4, 9, 9, 7, 6, 6, 2, 8, 6, 8, 5, 0, 2, 6, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
In this variant of the secretary problem, the applicants' values are independently distributed on a known interval, like in A242674; and the number of applicants is itself a random variable with uniform distribution on 1..n (and then the limit n -> infinity is taken), like in A325905. So we have more information than in the variant considered in A325905 but less information than in the variant considered in A242674. Hence A325905 < this constant < A242674. - Andrey Zabolotskiy, Sep 14 2019
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361.
LINKS
Steven R. Finch, Errata and Addenda to Mathematical Constants, Sec. 5.15 Optimal Stopping Constants, pp. 53-55, arXiv:2001.00578 [math.HO], 2020.
Zdzisław Porosiński, On best choice problems having similar solutions, Statistics & Probability Letters, 56 (2002), 321-327.
Eric Weisstein's MathWorld, Sultan's Dowry Problem
FORMULA
(1 - e^a)*Ei(-a) - (e^(-a) + a*Ei(-a))*(gamma + log(a) - Ei(a)), where a is A246664, gamma is Euler's constant and Ei is the exponential integral function.
EXAMPLE
0.43517080558012765805918991284785841042796259475347024702979123...
MATHEMATICA
a = x /. FindRoot[E^x*(1 - EulerGamma - Log[x] + ExpIntegralEi[-x]) - (EulerGamma + Log[x] - ExpIntegralEi[x]) == 1, {x, 2}, WorkingPrecision -> 102]; (1 - E^a)*ExpIntegralEi[-a] - (E^-a + a*ExpIntegralEi[-a])*(EulerGamma + Log[a] - ExpIntegralEi[a]) // RealDigits // First
CROSSREFS
Sequence in context: A292612 A316254 A029934 * A274260 A011397 A352692
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)