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%I #3 Mar 30 2012 17:35:16
%S 1,2,2,3,4,3,4,5,6,4,5,8,7,8,5,6,9,12,9,10,6,7,10,13,16,11,12,7,8,11,
%T 14,17,20,13,14,8,9,16,15,18,21,24,15,16,9,10,17,24,19,22,25,28,17,18,
%U 10,11,18,25,32,23,26,29,32,19,20,11,12,19,26,33,40,27,30,33,36,21,22,12
%N Table by antidiagonals, T(n,k) is k-th number that starts with n in binary representation.
%C In rows n through 2n-1, every integer >= n occurs exactly once.
%F T(n,1) = n; T(n,2k) = 2T(n,k); T(n,2k+1) = 2T(n,k) + 1. T(n,k) = k + (n-1) * 2^floor(log_2(k)) = k + (n-1)*A053644(k).
%e Top left corner is:
%e 1 2 3 4 5
%e 2 4 5 8 9
%e 3 6 7 12 13
%e 4 8 9 16 17
%e 5 10 11 20 21
%Y Rows: A000027, A004754, A004755, A004756, A004757, A004758, A004759. Algebraically, A053645 would be row zero, minus A080079 would be row minus one. See also A053644.
%K easy,nonn,tabl
%O 1,2
%A _Franklin T. Adams-Watters_, Oct 23 2006