[seqfan] Re: Another surprising omission from OEIS

[Andrew Weimholt]

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