[seqfan] Open problem (invitation)

[mathar]

Given an integer N>0, and after been found all the first N! terms of A217626,
you were asked find either a function or algorithm which counts the number of
different "trivial" palindromic patterns that could be built from these terms.

For example:

[1,9,2,9,1] is a "trivial" palindromic pattern.

But

[2,18,4,18,2] is not trivial, until it is re-written it as: [2,2*9,4,9*2,2]

So the "triviality" of such kind of patterns depends on the prime factorization
of their components. Such behavior can not be reproduced by the prime numbers.

I can not spot it yet "the how", but the study of this matter might have deep
implications in the number theory. (These patterns teach us how to build odd
numbers in a similar way as what described by the Goldbach's Conjecture for
the even numbers).

If you decide to face this friendly challenge,

Good Luck!!!

Sincerely, with regards:

R. J. Cano