On the periodic properties of self-decimated generators of pseudorandom   numbers
  We consider a self-decimated generator of pseudorandom numbers and examine the preperiod $\lambda$ and the period $\mu$ of its state sequence. We obtain the expectations and variances of $\lambda$ and $\mu$ for the case when decimation steps are chosen randomly and independently from the set {1,2}. 
Sergey Agievich, Oleg Solovey