The almost PV behavior of some far from PV algebraic integers

This paper studies divisibility properties of sequences defined inductively by n,=l, a n+1 =Sa,+tLea,], where s, t are integers, and 0 is a quadratic irrationality. Under appropriate hypotheses (especially that s + t0 be a PV-number) it is proved that the highest power of A that divides a,, where A is the discriminant of 19, tends to infinity. This is noteworthy in that truncation would normally be expected to destroy any simple algebraic structure: Moreover, we establish related results that imply the a, are not uniformly distributed modulo A in cases where the smaller conjugate of s + t0 exceeds 1 in modulus (the non-PV case).