If you moved the 3 at the end of a certain large number to the beginning, it would be the same as multiplying it by 3. What is the number?

(In reply to

re: complete set of answers, mathy reasoning *** correction by empraptor)

Argh... another correction - minor this time. The general formula is right the way I left it in my last correction.

It's just that I wrote last time that n=0 produces a solution that
satisfies the equation made to model the problem. That it
satifies the equation but is not a valid solution because that would
make X=0 and X wouldn't end with 3. But now I look and realize
X=0 DOESN'T satisfy the equation at all. So we're all the merrier
because we don't have to justify eliminating n=0 case with words.
The equation takes care of it.