[seqfan] Re: Xmas-challenge

[W. Edwin Clark]

Oops. Sorry about that.

On Sun, Dec 27, 2020 at 2:34 PM Rob Pratt <robert.william.pratt at gmail.com>
wrote:

> Those two both include 100.
>
> > On Dec 27, 2020, at 2:33 PM, W. Edwin Clark <wclark at mail.usf.edu> wrote:
> >
> > Here are two such chains each of length 77 from
> > https://fivethirtyeight.com/features/is-this-bathroom-occupied/ (scroll
> > down and you will see the chains). The complements of these two chains
> > consist of primes and semiprimes.
> >
> > A:=[93, 31, 62, 1, 87, 29, 58, 2, 92, 46, 23, 69, 3, 57, 19, 38, 76, 4,
> 68,
> > 34, 17, 85, 5, 35, 70, 10, 100, 50, 25, 75, 15, 45, 90, 30, 60, 20, 40,
> 80,
> > 16, 64, 32, 96, 48, 24, 12, 6, 78, 26, 52, 13, 91, 7, 49, 98, 14, 56, 28,
> > 84, 42, 21, 63, 9, 81, 27, 54, 18, 36, 72, 8, 88, 44, 22, 66, 33, 99, 11,
> > 55];
> >
> > B:=[62, 31, 93, 3, 69, 23, 46, 92, 4, 76, 38, 19, 95, 5, 65, 13, 52, 26,
> > 78, 6, 48, 96, 32, 64, 16, 80, 10, 70, 35, 7, 49, 98, 14, 56, 28, 84, 42,
> > 21, 63, 9, 81, 27, 54, 18, 36, 72, 24, 12, 60, 30, 90, 45, 15, 75, 25,
> 50,
> > 100, 20, 40, 8, 88, 44, 22, 66, 33, 99, 11, 55, 1, 87, 29, 58, 2, 68, 34,
> > 17, 85];
> >
> > The OEIS entry points to this link and several other papers on the topic.
> >
> >> On Sun, Dec 27, 2020 at 12:36 PM David Corneth <davidacorneth at gmail.com
> >
> >> wrote:
> >>
> >> Just some thoughts and naive observations. Most of these quotients are
> >> primes. A few are prime powers. Then some other stuff.
> >> Looking at the lcm of elements in that length 76 solution
> >> it's 6064949221531200 which is in A025487. Would it help predict the
> lcm of
> >> such a solution and take it's divisors <= n to see where that gets us?
> >>
> >>
> >>
> >> On Sun, Dec 27, 2020 at 1:32 PM Peter Luschny <peter.luschny at gmail.com>
> >> wrote:
> >>
> >>> Andrew Weimholt> ... here one of length 72 - probably not the max.
> >>>
> >>> This one has length 76:
> >>> [93, 31, 62, 1, 87, 29, 58, 2, 92, 46, 23, 69, 3, 57, 19, 38, 76, 4,
> 68,
> >>> 34, 17, 85, 5, 35, 70, 10, 50, 25, 75, 15, 45, 90, 30, 60, 20, 40, 80,
> >> 16,
> >>> 64, 32, 96, 48, 24, 12, 6, 78, 26, 52, 13, 91, 7, 49, 98, 14, 56, 28,
> 84,
> >>> 42, 21, 63, 9, 81, 27, 54, 18, 36, 72, 8, 88, 44, 22, 66, 33, 99, 11,
> 55]
> >>>
> >>> Can we characterize the elements of the complement?
> >>> {37,39,41,43,47,51,53,59,61,65,67,71,73,74,77,79,82,83,86,89,94,95,97}
> >>>
> >>> These are all primes or semiprimes. Note that in Andrew's
> >>> sequences there is also 2*5*7 in the complement set. Can one
> >>> understand this as an indication of non-optimality?
> >>>
> >>> Is the longest chain unique? Probably not. In this case I
> >>> will register the sequence: "Number of divisor chains with
> >>> maximum length".
> >>>
> >>> But one of the correspondents noted that there is uniqueness
> >>> in certain cases. However, it is not clear which these are.
> >>>
> >>> --
> >>> Seqfan Mailing list - http://list.seqfan.eu/
> >>>
> >>
> >> --
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> >>
> >
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>
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