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
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
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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
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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.