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

Thomas Scheuerle ts181 at mail.ru
Thu Aug 17 16:53:35 CEST 2023

```"In particular, it mentions a 9x9 square tiled with nine 3x3 squares, and a 15x15
square tiled with 15 3x5 rectangles. Can these solutions be obtained with the
permutation method?"

No, that's part of the point. It would work for 4x4 as 4 times a 2x2 square.

For composite odd numbers there exist at least some rectangle like solutions
but my mentioned approach (individual permutations on rows and columns ) does not bring us
directly from one solution to a new one.

That's what I meant by "hard to find".
I could imagine that there are sporadic solutions for some ? X ? exist
which cannot be generalized to other n x n.

Even numbers:  We can likely find a way from one solution to the next.
Odd numbers: A general method needs to be discovered. Maybe not such easy..

For odd numbers finding the first non-recatngle solution is maybe a kind of Rosetta-stone.
Did anybody find solutions which triangle like structures ?

best regards Thomas

```