[seqfan] Re: Xmas-challenge

Peter Luschny peter.luschny at gmail.com
Sun Dec 27 13:31:58 CET 2020


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.



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