# [seqfan] Re: Two make a palindrome

Alex M timeroot.alex at gmail.com
Sun Nov 10 05:35:46 CET 2013

```It's worth considering that, if there is a single integer missing, then an
infinite number of integers must be missing. For instance, if 697 is not in
the sequence, then 1679 could not be either (unless it came before all
numbers from 1 to 696 had been used), because immediately after 1679 would
come 697. Given that parenthetical, 1679 could still be in the sequence,
but only finitely many numbers can be in there before 11540, as Rob
calculated, so some would necessarily be excluded.

In binary this seems like an interesting parity problem - since a number
can be scrambled into a palindrome in binary iff either the number of 1s is
even or the number of 0s is even.
That seems like a problem where actually proving certain properties would
be possible.

~6 out of 5 statisticians say that the
number of statistics that either make
no sense or use ridiculous timescales
at all has dropped over 164% in the
last 5.62474396842 years.

On Sat, Nov 9, 2013 at 4:54 PM, Maximilian Hasler <
maximilian.hasler at gmail.com> wrote:

> Rob, Eric, SeqFans,
> I propose the sequence as https://oeis.org/draft/A228407 where I added
> a link to Rob's post/calculations, and also a list of "records of
> minima", i.e., (n,a(n)) where the least missing integers occur. Maybe
> these could become sequences on their own (the values and the indices
> separately) if further investigations in that sense are to be made.
> Regards,
> Maximilian
>
> > Le 9 nov. 2013 à 17:10, "Rob Arthan" <rda at lemma-one.com> a écrit :
> >
> >> Eric,
> >>
> >> That's a fun sequence and an interesting conjecture. As you say, it is
> not easy to calculate by hand. To get a feel
> >> for the conjecture I wrote an ML program to do it. This is what I got
> for the first 200 values:
> (...)
> >> My program is now in a loop printing out n, a(n) and m(n). The evidence
> currently supports your conjecture but m(n) is
> >> growing quite slowly:
> >>
> >>   a(5846) = 589, m(5846) = 598
> >>   a(5847) = 598, m(5846) = 679
> >>   ...
> >>   a(11539) = 1617, m(11539) = 679
> >>   a(11540) =  679 m(11540) = 697
> >>
> >> So 697 persisted as the smallest missing integer for more than 5,000
> stages. I will leave it running and report back if anything noteworthy
> occurs.
> >>
> >> Regards,
> >>
> >> Rob.
> >>
>
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>
```