[seqfan] Re: Xmas-challenge

[Rob Pratt]

76 is optimal.

> On 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/
>> 
> 
> --
> Seqfan Mailing list - http://list.seqfan.eu/