ABSTRACT. We study the properties and asymptotics of the Jacobi matrices associated with equilibrium measures of the weakly equilibrium Cantor sets. These family of Cantor sets were defined and different aspects of orthogonal polynomials on them were studied recently. Our main aim is numerically examine some conjectures concerning orthogonal polynomials which do not directly follow from previous results. We also compare our results with more general conjectures made for recurrence coefficients associated with fractal measures supported on R.