${a_n}$ for a sequence containing no zeroes Take the sequence of Natural numbers which do not contain the digit zero.
So your sequence becomes:
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12 ...
Can we find an expression for ${a_n}$ ?

There are $9^m$ members of $\{a_n\}$ with $m$ digits.
After that, the $(m+1)$-digit members of $\{a_n\}$
follow the rule that $a_n = a_{\left(n-9^m\right)} + 10^m.$
And then the pattern repeats.
