# [seqfan] Re: A055198 comment seems wrong

israel at math.ubc.ca israel at math.ubc.ca
Tue Mar 15 04:13:58 CET 2022

```The two orders will produce different, but essentially equivalent, results.
Let f and g be two maps. Then x_0 -> x_1 -> x_2 -> ... -> x_n = x_0 is a
periodic orbit under f o g if and only if g(x_0) -> g(x_1) -> ... -> g(x_n)
= g(x_0) is a periodic orbit under g o f. In the case at hand, take f to be
"+4" and g "reverse".

Cheers,
Robert

On Mar 14 2022, Sean A. Irvine wrote:

>Just to be clear I did "reverse(n+4)".
>
>I now tried "reverse(n)+4" but that gives completely different terms, but
>again does not seem finite.
>
>It perhaps has something to do with leading 0s.
>
>
>On Tue, 15 Mar 2022 at 15:21, Neil Sloane <njasloane at gmail.com> wrote:
>
>> The definition of A055198 involves the operation of "add 4 and reverse
>> digits" (see A003608)
>>
>> You said: Today I was looking at reproducing A055198 concerning
>> iteratively reverse and add 4.
>>
>> But the order matters!  Start with 6 and you get either 1 or 10.  Could
>> this explain the disagreement?
>>
>>
>> Best regards
>> Neil
>>
>> Neil J. A. Sloane, Chairman, OEIS Foundation.
>> Also Visiting Scientist, Math. Dept., Rutgers University,
>> Email: njasloane at gmail.com
>>
>>
>>
>> On Mon, Mar 14, 2022 at 10:12 PM Sean A. Irvine <sairvin at gmail.com>
>> wrote:
>>
>> > Hi,
>> >
>> > Today I was looking at reproducing A055198 concerning iteratively
>> > reverse and add 4.
>> >
>> > https://oeis.org/A055198
>> >
>> > The first comment seems to imply that the sequence is likely complete,
>> yet
>> > I find many more terms.
>> >
>> > For example, 1011 repeats after 90 iterations and so should be in the
>> > sequence. No term of the iteration is less than 1011.
>> >
>> > Likewise, 1013, 1015, and many other numbers.
>> >
>> > Sean.
>> >
>> > --
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>--
>Seqfan Mailing list - http://list.seqfan.eu/
>
>

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