Abstract: | For almost all x>1, (xn)(n=1,2,…) is equidistributed modulo 1, a classical result. What can be said on the exceptional set? It has Hausdorff dimension one. Much more: given an (bn) in 0,1 and ε>0, the x -set such that |xn−bn|<ε modulo 1 for n large enough has dimension 1. However, its intersection with an interval 1,X] has a dimension <1, depending on ε and X. Some results are given and a question is proposed. |