A246673 - OEIS

%I #14 Feb 16 2025 08:33:23

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

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

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

%N Decimal expansion of 'c', an optimal stopping 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 2*xi/(xi + 2), where xi is A246672.

%e 1.165623287731622772082152021107540408255491345963342103019...

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

%Y Cf. A246672.

%K nonn,cons,easy

%O 1,3

%A _Jean-François Alcover_, Sep 01 2014