[seqfan] Re: Xmas-challenge

[W. Edwin Clark]

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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