%I #6 Sep 08 2013 13:30:51
%S 1,1,1,1,2,1,1,3,3,1,1,4,4,4,1,1,5,4,4,5,1,1,6,5,4,5,6,1,1,7,7,5,5,7,
%T 7,1,1,8,8,8,6,8,8,8,1,1,9,8,8,8,8,8,8,9,1,1,10,9,8,8,8,8,8,9,10,1,1,
%U 11,11,9,8,8,8,8,9,11,11,1,1,12,12,12,9,8,8,8,9,12,12,12,1,1,13,12,12,13,9
%N Triangle T(n,k), 0<=k<=n : T(n,k)is smallest number such that T(n,k)>=T(n-1,k-1), T(n,k)>=T(n-1,k), T(n,k)and T(n-1,k-1)+T(n-1,k) have the same parity, T(0,0)=1 .
%C Sequence read mod 2 gives A047999 .
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 3, 3, 1;
%e 1, 4, 4, 4, 1;
%e 1, 5, 4, 4, 5, 1;
%e 1, 6, 5, 4, 5, 6, 1;
%e 1, 7, 7, 5, 5, 7, 7, 1;
%e 1, 8, 8, 8, 6, 8, 8, 8, 1;
%e 1, 9, 8, 8, 8, 8, 8, 8, 9, 1;
%Y Diagonals : A000012, A000027, A098181, A127932, A127934.
%K nonn,tabl
%O 0,5
%A _Philippe Deléham_, Apr 08 2007