Normal equivalencies for eventually periodic basic sequences

Researchers such as W.M. Schmidt, A.D. Pollington, and F. Schweiger have studied when normality with respect to one expansion is equivalent to normality with respect to another expansion. Following in their footsteps, we show that when QQ is an eventually periodic basic sequence, that QQ-normality and QQ-distribution normality are equivalent to normality in base bb where bb is dependent on QQ. We also show that boundedness of the basic sequence is not sufficient for this equivalence.