cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A322167 #29 May 30 2023 02:25:11
%S A322167 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,
%T A322167 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,
%U A322167 3,7,9,5,0,5,2,0,1,3,3
%N A322167 Decimal expansion of asymptotic probability of success in the returning secretary problem.
%H A322167 Bryn Garrod, Grzegorz Kubicki, and Michał Morayne, <a href="https://doi.org/10.1137/09076845X">How to choose the best twins</a>, Siam J. Discrete Math., Vol. 26, No. 1 (2012), pp. 384-398.
%H A322167 J. M. Grau Ribas, <a href="https://doi.org/10.1007/s10878-018-0349-8">A new look at the returning secretary problem</a>, Journal of Combinatorial Optimization, Vol. 37, No. 4 (2019), pp. 1216-1236.
%F A322167 Equals (1/3)*(-4 + 6*sqrt(1 - x) + 4*x + (-2 + 2*sqrt(1-x) + x)*log(x)) where x = A322166.
%e A322167 0.76797426727957343030182289371864503965422...
%p A322167 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
%t A322167 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 *)
%Y A322167 Cf. A322166.
%K A322167 nonn,cons
%O A322167 0,1
%A A322167 _José María Grau Ribas_, Nov 29 2018