Search: id:A101309
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%I A101309
%S A101309 0,1,0,1,0,0,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,1,1,
%T A101309 0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,
%U A101309 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.
%Y A101309 Sequence in context: A157687 A127266 A083923 this_sequence A141474 A073424 
               A135993
%Y A101309 Adjacent sequences: A101306 A101307 A101308 this_sequence A101310 A101311 
               A101312
%K A101309 nonn,tabl
%O A101309 0,1
%A A101309 Paul D. Hanna (pauldhanna(AT)juno.com), Dec 23 2004

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