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.

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, 13, 13, 16, 13, 10, 8, 9, 16, 15, 14, 20, 17, 14, 11, 9, 10, 18, 17, 23, 22, 21, 18, 15, 12, 10, 11, 20, 19, 24, 28, 24, 22, 19, 19, 13, 11, 12, 22, 21, 25, 32, 29

Offset

1,2

Comments

Each positive number k appears A122953(k) times in this array.

Links

Table of n, a(n) for n=1..72.

Rémy Sigrist, Perl program for A300302

Formula

T(n, 1) = n.

T(n, 2) = 2*n.

T(n, 3) = 2*n + 1.

T(1, n) = A000027(n).

T(2, n) = A062289(n).

T(3, n) = A004780(n).

T(4, n) = A004753(n).

T(5, n) = A004748(n).

T(6, n) = A004749(n).

T(7, n) = A004781(n).

T(8, n) = A004779(n-1).

T(10, n) = A132782(n).

Example

Square array begins:
  n\k|    1    2    3    4    5    6    7    8    9   10
  ---+--------------------------------------------------
    1|    1    2    3    4    5    6    7    8    9   10  <--  A000027
    2|    2    4    5    6    8    9   10   11   12   13  <--  A062289
    3|    3    6    7   11   12   13   14   15   19   22  <--  A004780
    4|    4    8    9   12   16   17   18   19   20   24  <--  A004753
    5|    5   10   11   13   20   21   22   23   26   27  <--  A004748
    6|    6   12   13   14   22   24   25   26   27   28  <--  A004749
    7|    7   14   15   23   28   29   30   31   39   46  <--  A004781
    8|    8   16   17   24   32   33   34   35   40   48  <--  A004779
    9|    9   18   19   25   36   37   38   39   41   50
   10|   10   20   21   26   40   41   42   43   52   53  <--  A132782

Prog

(Perl) See Links section.

Crossrefs

Cf. A000027, A004748, A004749, A004753, A004779, A004780, A004781, A062289, A122953, A132782.

Sequence in context: A032355 A308597 A205153 * A091257 A216622 A319840

Adjacent sequences: A300299 A300300 A300301 * A300303 A300304 A300305

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Mar 08 2018

Status

approved