Search: id:A122872
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%I A122872
%S A122872 1,2,2,3,4,3,4,5,6,4,5,8,7,8,5,6,9,12,9,10,6,7,10,13,16,11,12,7,8,11,14,
%T A122872 17,20,13,14,8,9,16,15,18,21,24,15,16,9,10,17,24,19,22,25,28,17,18,10,
%U A122872 11,18,25,32,23,26,29,32,19,20,11,12,19,26,33,40,27,30,33,36,21,22,12
%N A122872 Table by antidiagonals, T(n,k) is k-th number that starts with n in binary 
               representation.
%C A122872 In rows n through 2n-1, every integer >= n occurs exactly once.
%F A122872 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 A122872 Top left corner is:
%e A122872 1 2 3 4 5
%e A122872 2 4 5 8 9
%e A122872 3 6 7 12 13
%e A122872 4 8 9 16 17
%e A122872 5 10 11 20 21
%Y A122872 Rows: A000027, A004754, A004755, A004756, A004757, A004758, A004759. 
               Algebraically, A053645 would be row zero, minus A080079 would be 
               row minus one. See also A053644.
%Y A122872 Sequence in context: A106251 A134478 A051162 this_sequence A132919 A162619 
               A032355
%Y A122872 Adjacent sequences: A122869 A122870 A122871 this_sequence A122873 A122874 
               A122875
%K A122872 easy,nonn,tabl
%O A122872 1,2
%A A122872 Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 23 2006

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