I have a program on my computer that can convert a number from any base to any other base. I started with some number, converted it to another base, and the result was one digit shorter. Then I tried a different base, and the result was again one digit shorter.

Altogether I did this 10 times, and the number grew one digit shorter each time, so the final number was 10 digits shorter than the starting number. (The final number had more than 1 digit.)

What is the smallest number I could have started with?