Sequence A112088 without example

[Hugo Pfoertner]

Max wrote:
> 
> Rainer,
> 
> It is not clear to me how you defined your sequence either.
> What "minimum numbers" and what "game" you are talking about?
> Could you please clarify the definition of your sequence?
> 
> Thanks,
> Max

AFAIK, Rainer is talking about the Josephus Problem in its classical
form, where n people are arranged around the circumference of a circle.
An executioner walks around the circle without changing his direction
and without making shortcuts. Starting at the first person, every third
(of the remaining) persons on the circumference of the circle is
eliminated until only one person remains. The surviving persons remain
at their original positions in the circle. Therefore the executioner
needs to walk a certain amount of rounds until his job is done. Rainers
observation is that A112088(n) is the minimum number of people required
such that the executioner needs n rounds until only one survivor
remains.

It might be necessary to adjust the offset dependent on how exactly
"rounds" are counted. I prefer a rounds count, where the final survivor
counts the times he was passed by the executioner including the final
rendezvous.

Hugo Pfoertner

> 
> On 6/5/06, Rainer Rosenthal <r.rosenthal at web.de> wrote:
> > To SeqFan and to author Simon Strandgaard:
> >
> > Playing the "Josephus problem" with "every third out"
> > and denoting the minimum numbers in this game, I found
> >
> >      2, 3, 5, 7, 11, 16, 24, 36, 54, 81, ...
> >
> > I was happy to find them in this sequence:
> > http://www.research.att.com/~njas/sequences/A112088.
> >
> > My computed values are the same up to a(18) = 2082, so
> > that my Josephus game is likely to generate exactly
> > this sequence.
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