[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").
I wrote more about this on my Kaprekar page,
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.
>
> What's your opinion ?
>
> giovanni
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Robert Munafo -- mrob.com
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