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