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

0,1

Links

Table of n, a(n) for n=0..78.

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.

Formula

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

Example

0.76797426727957343030182289371864503965422...

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 *)

Crossrefs

Cf. A322166.

Sequence in context: A153857 A093813 A092902 * A245771 A202345 A010512

Adjacent sequences: A322164 A322165 A322166 * A322168 A322169 A322170

Keyword

nonn,cons

Author

José María Grau Ribas, Nov 29 2018

Status

approved