Normality preserving operations for Cantor series expansions and   associated fractals part II
  We investigate how non-zero rational multiplication and rational addition affect normality with respect to $Q$-Cantor series expansions. In particular, we show that there exists a $Q$ such that the set of real numbers which are $Q$-normal but not $Q$-distribution normal, and which still have this property when multiplied and added by rational numbers has full Hausdorff dimension. Moreover, we give such a number that is explicit in the sense that it is computable. 
Dylan Airey and Bill Mance and Joseph Vandehey
math.NT