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A246664 Decimal expansion of 'a', an auxiliary constant associated with the asymptotic probability of success in the secretary problem when the number of applicants is uniformly distributed. 2
2, 1, 1, 9, 8, 2, 4, 4, 0, 9, 8, 9, 2, 0, 6, 3, 6, 4, 9, 4, 6, 4, 0, 0, 5, 3, 8, 3, 0, 0, 7, 4, 0, 9, 1, 5, 4, 5, 5, 4, 4, 6, 3, 9, 6, 3, 2, 5, 3, 4, 1, 9, 8, 5, 4, 0, 9, 2, 0, 2, 7, 5, 4, 2, 6, 7, 6, 2, 7, 7, 4, 3, 8, 7, 1, 8, 5, 4, 8, 7, 9, 8, 2, 3, 9, 8, 7, 3, 8, 6, 2, 6, 6, 3, 0, 3, 2, 3, 8, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361.
LINKS
Eric Weisstein's MathWorld, Sultan's Dowry Problem.
Wikipedia, Secretary problem.
FORMULA
e^a*(1 - gamma - log(a) + Ei(-a)) - (gamma + log(a) - Ei(a)) = 1, where gamma is Euler's constant and Ei is the exponential integral function.
EXAMPLE
2.119824409892063649464005383007409154554463963253419854092...
MATHEMATICA
a /. FindRoot[E^a*(1 - EulerGamma - Log[a] + ExpIntegralEi[-a]) - (EulerGamma + Log[a] - ExpIntegralEi[a]) == 1, {a, 2}, WorkingPrecision -> 100] // RealDigits // First
CROSSREFS
Cf. A246665.
Sequence in context: A368924 A019803 A214506 * A229962 A141601 A108558
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)