cp's OEIS Frontend

A nim-multiplication table (A051775) of size 2^2^n can be compressed to a matrix of size 2^n, using Walsh permutations. As the nim-multiplication tables are submatrices to the bigger ones, also the compressions are submatrices to the bigger ones, leading to this infinite array.

This array is closely related to the nim-multiplication table powers of 2 (A223541). Both arrays can be seen as different views of the same cubic binary tensor.

The diagonal is A001317 (Sierpinski triangle rows read like binary numbers).

The elements of this array are listed in A223539. In the key-matrix A223538 the entries of this array (which become very large) are replaced by the corresponding index numbers of A223539. (Surprisingly, the key-matrix seems to be interesting on its own.)

List of entries in the compressed nim-multiplication table (A223537).

The first 1, 3, 9, 30, 108, 402, 1548, 6072, 24048, ... entries are the distinct entries of A223537-submatrices of size 1, 2, 4, 8, 16, 32, 64, 128, 256, ... (A000079).