[seqfan] Re: A070837

[Sascha Kurz]

I probably meant "at least 5 digits". But that is a long time ago.
Please replace my comment with something useful. The idea probably was
to give some information on the subsequent numbers without listing too
many of them.

Best,
Sascha

Am Donnerstag, den 23.07.2015, 15:57 +0200 schrieb Giovanni Resta:
> On 07/23/2015 11:35 AM, Christian Perfect wrote:
> > I've been computing a sequence which turned out to be A070837 - the
> > smallest k such that |k-R(k)|=9n, or 0 if no such k exists.
> > I found an error in a(21) - it was listed as 190, but |190-R(190)| is 9*11.
> > I've corrected it to 1090.
> > The comment by Sascha Kurz appears to be incorrect - should it say "at
> > least 5 digits"? 9n=18, k =13 is the first of many counterexamples to the
> > statement as I interpret it. The statement is true when changed to "at
> > least 5 digits".
> > We've compute values up to k=10^8, so my maximum n for which I'm sure of
> > a(n) is 11108889, but before I submit a b-file I want to check that the
> > zeroes in the published sequence are really zeroes. Can anyone help? The
> > first zero is at n=12. A scatter plot of the values I've computed strongly
> > suggests to me that every n has a non-zero k:
> > http://checkmyworking.com/misc/a070837.png
> 
> Kurz comment is not clear to me.
> 
> I hope you will not submit a b-file with 11108889 elements...
> Apart for sequences of exceptional significance, the usual upper limit
> for a b-file is 10000 entries.
> 
> Checking the zeros is not difficult, the only things to do is estimate
> the largest possible k that can give |k-R(k)|=9n.
> 
> It is easy to see that, if k has respectively 2, 3, 4, 5, 6, 7, 8, digits
> the minimum nonzero value of |k-R(k)| is respectively equal to
> 
> 2   9     (10 - 01)
> 3   99    (201 - 102)
> 4   90    (1101 - 1011)
> 5   990   (11001 - 10011)
> 6   900   (101001 - 100101)
> 7   9900  (1010001 - 1000101)
> 8   9000  (10010001 - 10001001)
> 9   99000 (100100001 - 100001001)
> 10  90000 (1000100001 - 1000010001)
> 
> a pattern clearly emerges.
> 
> This table helps understanding the upper bound for k when searching for 
> a certain 9n.
> For example, if we are interested in all
> the n < 10000, i.e., 9*n <= 89991,
> then we know that it is sufficient (and probably necessary) to
> test all k with up to 8 digits, i.e. k < 10^8.
> Indeed, k with 9 or 10 digits are not needed, since the minimum 
> difference for 9 digits is 99000 > 89991, and for 10 digits is 90000  > 
> 89991. (For 11 or more digits we expect the minimum difference to be 
> even larger).
> 
> so, to check the 76 values in Data representing differences up to 9*76 = 
> 684, checking k up to 9999 is enough.
> 
> Giovanni
> 
> 
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PD Dr. Sascha Kurz       TEL: -49-921-557353
LS Wirtschaftsmathematik FAX: -49-921-557352
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