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A300302 Square array T(n, k) (n >= 1, k >= 1) read by antidiagonals upwards: T(n, k) is the k-th positive number whose binary representation contains the binary representation of n as a substring.

%I A300302 #28 Mar 10 2018 07:14:36
%S A300302 1,2,2,3,4,3,4,6,5,4,5,8,7,6,5,6,10,9,11,8,6,7,12,11,12,12,9,7,8,14,
%T A300302 13,13,16,13,10,8,9,16,15,14,20,17,14,11,9,10,18,17,23,22,21,18,15,12,
%U A300302 10,11,20,19,24,28,24,22,19,19,13,11,12,22,21,25,32,29
%N A300302 Square array T(n, k) (n >= 1, k >= 1) read by antidiagonals upwards: T(n, k) is the k-th positive number whose binary representation contains the binary representation of n as a substring.
%C A300302 Each positive number k appears A122953(k) times in this array.
%H A300302 Rémy Sigrist, <a href="/A300302/a300302.pl.txt">Perl program for A300302</a>
%F A300302 T(n, 1) = n.
%F A300302 T(n, 2) = 2*n.
%F A300302 T(n, 3) = 2*n + 1.
%F A300302 T(1, n) = A000027(n).
%F A300302 T(2, n) = A062289(n).
%F A300302 T(3, n) = A004780(n).
%F A300302 T(4, n) = A004753(n).
%F A300302 T(5, n) = A004748(n).
%F A300302 T(6, n) = A004749(n).
%F A300302 T(7, n) = A004781(n).
%F A300302 T(8, n) = A004779(n-1).
%F A300302 T(10, n) = A132782(n).
%e A300302 Square array begins:
%e A300302   n\k|    1    2    3    4    5    6    7    8    9   10
%e A300302   ---+--------------------------------------------------
%e A300302     1|    1    2    3    4    5    6    7    8    9   10  <--  A000027
%e A300302     2|    2    4    5    6    8    9   10   11   12   13  <--  A062289
%e A300302     3|    3    6    7   11   12   13   14   15   19   22  <--  A004780
%e A300302     4|    4    8    9   12   16   17   18   19   20   24  <--  A004753
%e A300302     5|    5   10   11   13   20   21   22   23   26   27  <--  A004748
%e A300302     6|    6   12   13   14   22   24   25   26   27   28  <--  A004749
%e A300302     7|    7   14   15   23   28   29   30   31   39   46  <--  A004781
%e A300302     8|    8   16   17   24   32   33   34   35   40   48  <--  A004779
%e A300302     9|    9   18   19   25   36   37   38   39   41   50
%e A300302    10|   10   20   21   26   40   41   42   43   52   53  <--  A132782
%o A300302 (Perl) See Links section.
%Y A300302 Cf. A000027, A004748, A004749, A004753, A004779, A004780, A004781, A062289, A122953, A132782.
%K A300302 nonn,base,tabl
%O A300302 1,2
%A A300302 _Rémy Sigrist_, Mar 08 2018