Base Rep Puzzle

[Graeme McRae]

By dumb trial and error for n=2,3,... I get 1,2,9,81,1024,16384,1953125. 
The way to find element n of this sequence is to make a list of powers of 
2..n, and then find the smallest power, x, such that floor(ln(x)/ln(k)) is 
different for each k in 2..n.  This sequence is not in OEIS.
--Graeme

----- Original Message ----- 
From: "Hans Havermann" <pxp at rogers.com>
To: "David Wilson" <davidwwilson at comcast.net>; <seqfan at ext.jussieu.fr>
Sent: Wednesday, December 28, 2005 7:23 AM
Subject: Re: Base Rep Puzzle


>> 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).
>