A322167 Decimal expansion of asymptotic probability of success in the returning secretary problem.

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

Offset: 0

Author

José María Grau Ribas, Nov 29 2018

Keywords

• nonn
• cons

Examples

			0.76797426727957343030182289371864503965422...
		

Links

• Bryn Garrod, Grzegorz Kubicki, and Michał Morayne, How to choose the best twins, Siam J. Discrete Math., Vol. 26, No. 1 (2012), pp. 384-398.
• J. M. Grau Ribas, A new look at the returning secretary problem, Journal of Combinatorial Optimization, Vol. 37, No. 4 (2019), pp. 1216-1236.

Crossrefs

Cf. A322166.

Programs

Maple

x:=2/LambertW(2*exp(5)): evalf[90]((1/3)*(-4+6*sqrt(1-x)+4*x+(-2+2*sqrt(1-x)+x)*log(x))); # Muniru A Asiru, Dec 21 2018

Mathematica

With[{x = 2/ProductLog[2*Exp[5]]}, RealDigits[(6*Sqrt[1 - x] + 4*x - 4 + (2*Sqrt[1 - x] + x - 2)*Log[x])/3, 10, 120][[1]]] (* Amiram Eldar, May 30 2023 *)

Formula

Equals (1/3)*(-4 + 6*sqrt(1 - x) + 4*x + (-2 + 2*sqrt(1-x) + x)*log(x)) where x = A322166.