%I
%S 1,2,3,4,5,7,8,9,11,13,15,17,19,23,33
%N Descending squares: which squares can be packed with at least 2 squares so that every square directly above a square is strictly smaller? It is conjectured that the answer is all except those in this sequence.
%H E. Friedman, <a href="https://erichfriedman.github.io/mathmagic/1103.html">Illustrations</a>
%e 6, 10 and 25 are not in the sequence: To pack a 6 X 6 square, use 2 3 X 3s on the bottom, 3 2 X 2's above that and 6 1 X 1's on the top. For 10 X 10, use 2 5 X 5s on the bottom, a 4 X 4 and 2 3 X 3s above that; put 4 1 X 1's above the 4 X 4 and 3 2 X 2's above the 3 X 3s. For 25 X 25, use a 15 X 15 and a 10 X 10 on the bottom and 2 5 X 5s above the 10 X 10; above that use a 7 X 7, a 6 X 6 and 3 4 X 4s; the rest can be packed with 3 X 3s, 2 X 2's and 1 X 1's.
%K nonn,fini,full
%O 1,2
%A _Erich Friedman_, Oct 19 2003
%E Edited by _Dean Hickerson_, Oct 24 2003
