A246672 - OEIS

%I #15 Feb 16 2025 08:33:23

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

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

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

%N Decimal expansion of 'xi', an optimal stopping auxiliary constant associated with the two choice case.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361.

%H David Assaf, Larry Goldstein, Ester Samuel-Cahn, <a href="http://arxiv.org/abs/math/0510242">Two choice optimal stopping.</a>

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 46.

%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>.

%F Unique positive solution of (2/xi + 1)*log(xi/2 + 1) = 3/2.

%e 2.79399765260155079609907114136685042580083911662734211613515983...

%t xi /. FindRoot[(2/xi + 1)*Log[xi/2 + 1] == 3/2, {xi, 3}, WorkingPrecision -> 102] // RealDigits // First

%Y Cf. A246673.

%K nonn,cons,easy,changed

%O 1,1

%A _Jean-François Alcover_, Sep 01 2014