On the longest block in Lüroth expansion

In this paper, for a finite subset A⊂{2,3,⋯}, we introduce the notion of longest block function Ln(x,A) for the Lüroth expansion of x∈[0,1) with respect to A and consider the asymptotic behavior of Ln(x,A) as n tends to ∞. We also obtain the Hausdorff dimensions of the level sets and exceptional set arising from the longest block function.