A242673 - OEIS

%I #10 Feb 16 2025 08:33:22

%S 8,0,4,3,5,2,2,6,2,8,4,5,6,3,7,5,8,4,6,5,4,6,3,8,5,8,7,7,8,4,0,7,0,5,

%T 5,1,0,4,2,7,1,6,9,8,5,7,8,6,6,4,2,1,5,8,6,5,6,5,4,4,7,8,2,7,2,0,9,1,

%U 3,6,5,8,9,2,1,0,1,3,1,9,3,6,3,1,4,4,6,7,4,3,4,6,3,8,1,5,2,9,9,4

%N Decimal expansion of the unique real solution of the equation Ei(x)-gamma-log(x) = 1, where Ei is the exponential integral function and gamma the Euler-Mascheroni constant.

%C This constant is an auxiliary constant used in computing the asymptotic probability of success in one of the Secretary problems.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15, p. 362.

%H Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SultansDowryProblem.html">Sultan's Dowry Problem.</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Secretary_problem">Secretary problem</a>.

%e 0.804352262845637584654638587784070551...

%t a = x /. FindRoot[ExpIntegralEi[x] - EulerGamma - Log[x] == 1, {x, 1}, WorkingPrecision -> 105]; RealDigits[a, 10, 100] // First

%Y Cf. A054404, A242672, A242674.

%K nonn,cons,changed

%O 0,1

%A _Jean-François Alcover_, May 20 2014