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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.

%I A246664 #15 Feb 16 2025 08:33:23
%S A246664 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,
%T A246664 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,
%U A246664 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
%N 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.
%D A246664 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361.
%H A246664 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 45.
%H A246664 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SultansDowryProblem.html">Sultan's Dowry Problem.</a>
%H A246664 Wikipedia, <a href="http://en.wikipedia.org/wiki/Secretary_problem">Secretary problem</a>.
%F A246664 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.
%e A246664 2.119824409892063649464005383007409154554463963253419854092...
%t A246664 a /. FindRoot[E^a*(1 - EulerGamma - Log[a] + ExpIntegralEi[-a]) - (EulerGamma + Log[a] - ExpIntegralEi[a]) == 1, {a, 2}, WorkingPrecision -> 100] // RealDigits // First
%Y A246664 Cf. A246665.
%K A246664 nonn,cons,easy
%O A246664 1,1
%A A246664 _Jean-François Alcover_, Sep 01 2014