[seqfan] Re: Another surprising omission from OEIS

[Andrew Weimholt]

To be more precise, my example

  x*b^0 + x*b^1 + x*b^2 + ... + x*b^k, where x>0, b>1, k>1

should be rewritten as

  x*b^0 + x*b^1 + x*b^2 + ... + x*b^k, where x>0, b>x, k>1

Andrew

On Wed, Nov 11, 2009 at 12:12 AM, Andrew Weimholt
<andrew.weimholt at gmail.com> wrote:
> On Tue, Nov 10, 2009 at 9:16 PM,  <franktaw at netscape.net> wrote:
>
>> Should this sequence include 0 (000  in any base)?
>
> I'm not sure. It seems logical, but at the same time, a lot of
> sequences would be different if we allowed an arbitrary number of
> leading zeros. For instance, should 1000 be a considered a palindromic
> number because it could be written 0001000? Conversely, should 111 be
> disqualified as a repdigit because it could be written 0000111? The
> fact that 000 can be used to represent 0 is an artifact of our syntax
> for representing numbers. If we try to define the concept of a number
> being a "repdigit with length >2 in some base" with more mathematical
> rigor, we come up with something like this...
>
> Numbers that can be put in the form:
> x*b^0 + x*b^1 + x*b^2 + ... + x*b^k, where x>0, b>1, k>1
>
> ...which disqualifies 000.
>
> That said, I still haven't convinced myself that 0 ought to be
> excluded, because it depends on how we define this sequence and on the
> definition of "repdigit". Does the term "repdigit" need to be defined
> by a mathematical expression as the one above, or do we merely define
> it as a string of symbols that can be understood to represent a
> number? In the latter case, 000 qualifies.
>
> Anyone else want to weigh in before I submit the sequence?
>
> Andrew
>