Base Rep Puzzle

[Hans Havermann]

> For n >= 2, what is the smallest positive integer that has a  
> different number of digits in each of the bases 2 through n?

If I'm understanding this correctly (and doing it right), I get for  
bases 2 through 36, (base - 1) ^ {1, 1, 2, 4, 7, 9, 12, 15, 18, 21,  
25, 28, 32, 35, 39, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 83, 87,  
91, 95, 100, 104, 109, 113, 118, 122}. Except for an additional 1 at  
the start, these numbers match A031435 (reversal point for powers of  
consecutive natural numbers).