cp's OEIS Frontend

The large value for the 6-palindrome case, a(6)=2853326516320, has 139 as the smallest of the three bases.

Coincidentally, the following much shorter term, a(7)= 3360633, involves base 9 through 11, the conjunction of base-9 and base-10 palindromes (A029965) comes up a term short (assuming space limitations remain as they are at the beginning of 2011), and A053740 is a totally unrelated collection of palindromes that also contains 33633.

a(8) > 10^18. - Hiroaki Yamanouchi, Aug 22 2015

Say that a tiling of a rectangle by other rectangles is prime if the only sub-rectangles in the tiling are those formed by a single tile. Say that two tilings are equivalent if there exists an inclusion/overlap-preserving bijection between the vertices, edges, and faces of every rectangle in them.

Problem 69 in Hugo Steinhaus's One Hundred Problems In Elementary Mathematics asks the reader to show that a(3) = a(4) = 0, and that there exist prime dissections for 5, 7, and 8 in which the pieces are of equal area. It cites Czesław Ryll-Nardzewski as proving that a(6) = 0, though this is not difficult to show by hand. The book also provides diagrams of both n = 7 solutions and four of the six n = 8 solutions.

Chung et al.'s paper Tiling Rectangles with Rectangles shows that the sequence grows at least as fast as c*2^(n/7) for some positive constant c, and states without proof that it is bounded above by 20000^n.