The goal is to calculate
pvr(n, b, c)
	the number of "place value representations"
	of n in base b using digits from c.

define
pve(s, b, c) = \sum_{i \in |s|} s(i)b^i
pvp(n, b, c) = \set{s}{n = pve(s,b,c), s \in c^{<\omega}}
pvr(n, b, c) = |pvp(n, b, c)|

the brute force approach is to exhaustively list strings s with multiples
from c, evaluate them and then count the number of occurences of each value.
However, in practice the list of s will be finite and therefore there will be
some numbers whose occurrences in the list up to that point will be fewer
than pvr(n, b, c).

For example let b=2, c=3 and say the list of s stops at 100.
Then pve(100, 2, 3) = 4, but pve(22, 2, 3) = 6.
Further 22 < 100 lexicographically in 3^{<\omega},
therefore six will be counted, but not pvr(6, 2, 3) times.
In particular 110 will not be counted.