[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
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