A223542 Key-matrix of A223541 (nim-products of powers of 2) read by antidiagonals.

0, 1, 1, 3, 2, 3, 5, 5, 5, 5, 9, 7, 4, 7, 9, 11, 11, 6, 6, 11, 11, 15, 13, 15, 8, 15, 13, 15, 19, 19, 19, 19, 19, 19, 19, 19, 27, 23, 17, 23, 10, 23, 17, 23, 27, 29, 29, 21, 21, 12, 12, 21, 21, 29, 29, 33, 31, 33, 25, 16, 14, 16, 25, 33, 31

Offset: 0

Author

Tilman Piesk, Mar 21 2013

Keywords

• nonn
• tabl

Comments

Matrix A223541 has very large entries, which are listed in A223543. This matrix has the same pattern as A223541, but the actual entries are replaced by the index numbers of A223543. Surprisingly, although it is just a helper, the key-matrix is mathematically interesting on its own. (See the fractal patterns in the SVG files of the binary and the ternary dual matrix.) Its diagonal is A006046-1.

Links

• Tilman Piesk, First 128 rows of the matrix, flattened
• Tilman Piesk, 256x256 key-matrix
• Tilman Piesk, Elements of binary dual matrix (13 SVGs)
• Tilman Piesk, Elements of ternary dual matrix (8 SVGs)
• Tilman Piesk, Walsh permutation; nimber multiplication (Wikiversity)

Crossrefs

A223541, A223543, A006046

Formula

A223541(m,n) = A223543( a(m,n) ).

Diagonal: a(n,n) = A006046(n+1)-1.