n-digit numbers with n factors, each with a different number of digits

[Joshua Zucker]

Based on a problem from a recent Mandelbrot competition, which asked
something like:
what is the smallest composite number such that each of its factors
has a different number of digits?

I thought it might be fun to start working on the sequence of numbers
whose factors each have a different number of digits.

But then I thought it might be even more fun to find the smallest
n-digit number that has exactly n factors, each with a different
number of digits.

1, 11, 121, 1111, 14641, 112211, 1771561, 11117777, 123187801,
1464143923, 25937424601, ...

I'm of the opinion that this is interesting enough to share here but
not interesting or useful enough to submit to OEIS, but if a couple
people disagree then I'll work out some more terms and send it in.

--Joshua Zucker