cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A223538 Key-matrix of compressed nim-multiplication table (A223537) read by antidiagonals.

Original entry on oeis.org

0, 1, 1, 3, 2, 5, 5, 5, 7, 7, 9, 7, 4, 3, 25, 11, 11, 6, 6, 15, 15, 15, 13, 20, 8, 22, 20, 28, 20, 20, 25, 25, 28, 28, 17, 17, 30, 25, 17, 15, 10, 17, 19, 22, 68, 32, 32, 22, 22, 12, 12, 24, 24, 86, 86, 36, 34, 40, 28, 16, 14, 21, 27, 90, 104
Offset: 0

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Author

Tilman Piesk, Mar 21 2013

Keywords

Comments

Matrix A223537 has very large entries, which are listed in A223539. This matrix has the same pattern as A223537, but the actual entries are replaced by the index numbers of A223539. 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 dual matrix.) There is even a connection between the binary digits of the actual matrix (A223537) and its key-matrix: It seems that for all matrices of size 8 or bigger the highest binary digits in the actual matrix are less than or equal to the highest binary digits in the key-matrix. (For technical reasons this is shown in the links section.)

Links

Crossrefs

Cf. A223537, A223539.

Formula

A223537(m,n) = A223539(a(m,n)).

A223539 List of entries in the compressed nim-multiplication table (A223537).

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 10, 12, 15, 16, 17, 32, 34, 48, 51, 64, 68, 80, 85, 96, 128, 136, 160, 170, 176, 192, 204, 208, 240, 255, 256, 257, 512, 514, 768, 771, 1024, 1028, 1280, 1285, 2048, 2056, 2560, 2570, 3072, 3084, 3840, 3855, 4096, 4112, 4352
Offset: 1

Views

Author

Tilman Piesk, Mar 21 2013

Keywords

Comments

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).

Examples

			Biggest entry of 8 X 8 submatrix of A223537 is A223537(7,7) = a(29) = 255.
Biggest entry of 16 X 16 submatrix of A223537 is A223537(15,15) = a(107) = 65535.

Links

Crossrefs

Cf. A223537, A223538.

Formula

A223537(m,n) = a(A223538(m,n)).
Showing 1-2 of 2 results.

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