[seqfan] Re: A055198 comment seems wrong
Neil Sloane
njasloane at gmail.com
Fri Mar 18 18:27:33 CET 2022
I deleted both versions of the false conjecture from A055198.
Now could someone please edit the entry and add a summary of what we know
now? Hans, for example?
And maybe add a b-file?
Thanks!
Best regards
Neil
Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com
On Fri, Mar 18, 2022 at 12:07 PM Hans Havermann <gladhobo at bell.net> wrote:
> Maximilian: "... This shows that there are 22 new cycles here,
> respectively represented by all odd numbers from 1011 to 1053. The next
> cycle contains only numbers larger than 10000."
>
> Each of those new cycles contains 90 terms, so we have now a b-file of
> 90*22+54 terms:
>
> http://chesswanks.com/seq/b055198.txt
>
> I think that the author's assertion that "all integers <= 10000" iterate
> to a cycle of the first 54 might have been a typo: 10000 = 1000. That's a
> lot easier than looking for some definitional issue or programming mishap.
> His "99889" maximum for the 111 trajectory can be understood by treating
> half-iteration (+4 without the digits-reversal) results as part of the
> domain (although clearly not part of the trajectory since he states the
> correct number of iterations).
>
> Why posit the conjecture without attempting some four-digit evolutions
> which would have revealed the additional cycles? Perhaps because (in its
> long run) the trajectory of 111 runs into plenty of both four- and
> five-digit integers that end up in the 54-cycle.
>
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