[seqfan] Re: Need help finding prime index values for sequence A363381

[Thomas Scheuerle]

Hello,

I expect that it is already very difficult to find solutions for any odd n.
Why ?
I observed that most solutions can be found with some approach:
First we start with shapes identical to rows or columns.
If we then apply individual permutations inside rows and inside columns such that each
of these permutations moves all elements the same absolute distance, then this approach can find solutions.
If we investigate this case then we find that such permutations are generally even.
That means they are a product of an even number of independent element swaps and can therefore only exist over
an even number of elements.
Therefore I conjecture if only solutions exist which can be reached by such permutations, then
The only solutions for odd p in a p x p matrix will be rows or columns as shapes.

Best regards

Thomas