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A246667 Decimal expansion of 'b', an auxiliary constant associated with the asymptotic probability of success in the full information version of the secretary problem.

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%I A246667 #15 Feb 16 2025 08:33:23
%S A246667 1,3,4,5,0,1,6,6,1,7,0,2,1,9,9,6,9,8,4,4,9,0,5,7,9,9,1,9,9,9,8,6,9,1,
%T A246667 5,0,1,5,3,8,7,5,8,4,2,0,6,0,6,3,6,7,5,4,1,6,2,8,7,2,6,1,0,5,7,9,1,3,
%U A246667 1,4,6,4,9,5,5,9,7,2,0,5,8,8,3,9,0,5,8,1,8,7,3,7,8,3,8,9,8,6,5,9,4
%N A246667 Decimal expansion of 'b', an auxiliary constant associated with the asymptotic probability of success in the full information version of the secretary problem.
%D A246667 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361.
%H A246667 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 45.
%H A246667 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SultansDowryProblem.html">Sultan's Dowry Problem.</a>
%H A246667 Wikipedia, <a href="http://en.wikipedia.org/wiki/Secretary_problem">Secretary problem</a>.
%F A246667 Ei(-b) - gamma - log(b) = -1, where gamma is Euler's constant and Ei is the exponential integral function.
%e A246667 1.3450166170219969844905799199986915015387584206063675416287261...
%t A246667 b /. FindRoot[ExpIntegralEi[-b] - EulerGamma - Log[b] == -1, {b, 2}, WorkingPrecision -> 101] // RealDigits // First
%Y A246667 Cf. A246668.
%K A246667 nonn,cons,easy
%O A246667 1,2
%A A246667 _Jean-François Alcover_, Sep 01 2014