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.
%I A223538 #28 Mar 14 2021 15:24:31 %S A223538 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, %T A223538 20,20,25,25,28,28,17,17,30,25,17,15,10,17,19,22,68,32,32,22,22,12,12, %U A223538 24,24,86,86,36,34,40,28,16,14,21,27,90,104 %N A223538 Key-matrix of compressed nim-multiplication table (A223537) read by antidiagonals. %C A223538 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.) %H A223538 Tilman Piesk, <a href="/A223538/b223538.txt">First 128 rows of the matrix, flattened</a> %H A223538 Tilman Piesk, <a href="/A223538/a223538.txt">256x256 key-matrix</a> %H A223538 Tilman Piesk, <a href="http://commons.wikimedia.org/wiki/Category:Compressed_nim-multiplication_table;_key_matrix;_dual">Elements of dual matrix</a> (15 SVGs) %H A223538 Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Walsh_permutation;_nimber_multiplication">Walsh permutation; nimber multiplication</a> (Wikiversity) %H A223538 . %H A223538 Connection between binary digits of A223537 (M) and the key matrix (KM): %H A223538 Let M_n (KM_n) denote the matrix of binary digits with exponent n in matrix M (KM). %H A223538 <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_dual;_255.svg">M_255(0..255,0..255)</a> <= <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_key_matrix;_dual;_14.svg">KM_14(0..255,0..255)</a> %H A223538 <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_dual;_127.svg">M_127</a>(0..127,0..127) <= <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_key_matrix;_dual;_12.svg">KM_12</a>(0..127,0..127) %H A223538 <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_dual;_063.svg">M_63</a>(0..63,0..63) <= <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_key_matrix;_dual;_10.svg">KM_10</a>(0..63,0..63) %H A223538 <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_dual;_031.svg">M_31</a>(0..31,0..31) <= <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_key_matrix;_dual;_08.svg">KM_8</a>(0..31,0..31) %H A223538 <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_dual;_015.svg">M_15</a>(0..15,0..15) <= <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_key_matrix;_dual;_06.svg">KM_6</a>(0..15,0..15) %H A223538 <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_dual;_007.svg">M_7</a>(0..7,0..7) <= <a href="http://commons.wikimedia.org/wiki/File:Compressed_nim-multiplication_table;_key_matrix;_dual;_04.svg">KM_4</a>(0..7,0..7) %H A223538 However, this row does not continue for the matrices of size 4, 2 and 1. %F A223538 A223537(m,n) = A223539(a(m,n)). %Y A223538 Cf. A223537, A223539. %K A223538 nonn,tabl %O A223538 0,4 %A A223538 _Tilman Piesk_, Mar 21 2013