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

0,4

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)

Formula

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

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

Crossrefs

A223541, A223543, A006046

Sequence in context: A130727 A155515 A023605 * A182003 A347266 A050060

Adjacent sequences: A223539 A223540 A223541 * A223543 A223544 A223545

Keyword

nonn,tabl

Author

Tilman Piesk, Mar 21 2013

Status

approved