A223537 Compressed nim-multiplication table read by antidiagonals.

1, 2, 2, 4, 3, 8, 8, 8, 12, 12, 16, 12, 5, 4, 192, 32, 32, 10, 10, 64, 64, 64, 48, 128, 15, 160, 128, 240, 128, 128, 192, 192, 240, 240, 80, 80, 256, 192, 80, 64, 17, 80, 96, 160, 20480, 512, 512, 160, 160, 34, 34, 176, 176, 40960, 40960, 1024

Offset

0,2

Comments

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.)

Links

Tilman Piesk, First 128 rows of the matrix, flattened

Tilman Piesk, Elements of dual matrix (256 SVGs)

Tilman Piesk, Walsh permutation; nimber multiplication (Wikiversity)

Tilman Piesk, MATLAB functions cv2cm and cm2cv

Formula

a(m,n) = A223539( A223538(m,n) ).

a(n,n) = A001317(n).

a(1,n) = A134683(n+1).

Prog

( Calculation of this matrix B from matrix A = A223541 with MATLAB: )
B = bin([256 256], 'pre') ;
for m=1:256
    B(m, 1:256) = cm2cv(  cv2cm( A(m, 1:256) )' ) ;
end
( The functions are linked above. See also the MATLAB code for A223541. )

Crossrefs

Cf. A051775, A223541, A001317, A223539, A223538.

Sequence in context: A005176 A050335 A360686 * A140860 A019681 A241580

Adjacent sequences: A223534 A223535 A223536 * A223538 A223539 A223540

Keyword

nonn,tabl

Author

Tilman Piesk, Mar 21 2013

Status

approved