# [seqfan] Re: Is 0001 a 4-digit base 10 number ?

Robert Munafo mrob27 at gmail.com
Fri Aug 19 23:30:57 CEST 2011

```This kind of problem is evident in the Kaprekar numbers (for example 45*45 =
2025 and 20+25=45).

The naive approach to Kaprekar numbers would allow parts that start with 0,
like 99*99=9801 and 98+01=99. This in turn leads to claims that for example
"04879" is a Kaprekar number because 04879*04879=0023804641 and
00238+04641=04879. This is a use of leading zeros that appears in A006886,
whose definition avoids the problem by not making reference to "the number
of digits". Compare to A045913 (which also doesn't mention "digits").

http://mrob.com/pub/math/seq-kaprekar.html

On Thu, Aug 18, 2011 at 10:18, Giovanni Resta <giovanni.resta at iit.cnr.it>wrote:

> My question arises from the description of A126364
> ( http://oeis.org/A126364 ) :
>
> Number of base 10 n-digit numbers with adjacent digits differing by one or
> less.
> 1, 10, 28, 80, 230, 664,...
>
> It seems clear, from a(2)=28, that the author counts 00 and 01 among
> the 2-digit base 10 numbers.
>
> It seems to me a little unusual, but I may be wrong.
>