A360633 Square array A(n, k), n, k > 0, read by antidiagonals upwards; A(n, k) = A360613(2*n-1) * A360613(2*k).

1, 2, 3, 4, 6, 5, 7, 12, 10, 8, 9, 21, 20, 16, 11, 13, 27, 35, 32, 22, 15, 14, 39, 45, 56, 44, 30, 17, 18, 42, 65, 72, 77, 60, 34, 19, 23, 54, 70, 104, 99, 105, 68, 38, 24, 25, 69, 90, 112, 143, 135, 119, 76, 48, 29, 26, 75, 115, 144, 154, 195, 153, 133, 96, 58, 31

Offset: 1

Author

Rémy Sigrist, Feb 14 2023

Keywords

• nonn
• tabl

Comments

This sequence can be seen as a greedy multiplication table where we alternately add rows and columns so that all products are distinct.

Conjecture: all integers appear in this sequence.

Examples

			Array A(n, k) begins:
  n\k |  1   2    3    4    5    6    7    8    9   10
  ----+-----------------------------------------------
    1 |  1   3    5    8   11   15   17   19   24   29
    2 |  2   6   10   16   22   30   34   38   48   58
    3 |  4  12   20   32   44   60   68   76   96  116
    4 |  7  21   35   56   77  105  119  133  168  203
    5 |  9  27   45   72   99  135  153  171  216  261
    6 | 13  39   65  104  143  195  221  247  312  377
    7 | 14  42   70  112  154  210  238  266  336  406
    8 | 18  54   90  144  198  270  306  342  432  522
    9 | 23  69  115  184  253  345  391  437  552  667
   10 | 25  75  125  200  275  375  425  475  600  725
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10011
• Rémy Sigrist, C program

Crossrefs

Cf. A249327, A360613, A360627, A360628.

Programs

C

See Links section.

Formula

A(n, k) = A360627(n) * A360628(k).

A(n, 1) = A360627(n).

A(1, k) = A360628(k).