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 A101309 #4 Mar 30 2012 18:36:44 %S A101309 0,1,0,1,0,0,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,1, %T A101309 1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0, %U A101309 0,1,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0 %N A101309 Matrix logarithm of A047999 (Pascal's triangle mod 2). %C A101309 Row sums equal A000120 (binary 1's-counting sequence). Antidiagonal sums form A101979. %F A101309 T(n, k)=1 when n XOR k = 2^m for integer m>=0, T(n, k)=0 elsewhere. %e A101309 T(n,k)=1 when n XOR k is a power of 2: %e A101309 T(3,2)=1 since 3 XOR 2 = 2^0, T(4,0)=1 since 4 XOR 0 = 2^2, %e A101309 T(5,1)=1 since 5 XOR 1 = 2^2, T(6,4)=1 since 6 XOR 4 = 2^2. %e A101309 Rows begin: %e A101309 [0], %e A101309 [1, 0], %e A101309 [1,0, 0], %e A101309 [0,1, 1,0], %e A101309 [1,0,0,0, 0], %e A101309 [0,1,0,0, 1,0], %e A101309 [0,0,1,0, 1,0,0], %e A101309 [0,0,0,1, 0,1,1,0],... %o A101309 (PARI) T(n,k)=if(n>k&bitxor(n,k)==2^valuation(bitxor(n,k),2),1,0) %Y A101309 Cf. A047999, A101979. %K A101309 nonn,tabl %O A101309 0,1 %A A101309 _Paul D. Hanna_, Dec 23 2004