Contributions to digit expansions with respect to linear recurrences

Abstract Extensions and improvements of a recent paper, “On Digit Expansions with Respect to Linear Recurrences” by A. Petho and R. F. Tichy (J. Number Theory 33 (1989), 243–256) are established. Furthermore distribution properties mod 1 of the sequence (xsG(n)) are investigated, where sG(n) denotes the sum-of-digits function with respect to the linear recurrence G.