A366303 Square array A(n, k), n, k > 0, read and filled by upwards antidiagonals the greedy way with distinct positive integers such that any two distinct terms in the same row or column are coprime.

1, 2, 3, 5, 7, 4, 9, 8, 11, 13, 17, 19, 21, 15, 23, 29, 25, 31, 37, 41, 35, 43, 47, 53, 14, 59, 61, 67, 49, 71, 65, 73, 55, 79, 83, 89, 97, 101, 103, 107, 6, 109, 113, 127, 121, 131, 137, 139, 149, 119, 143, 151, 157, 163, 167, 169, 173, 179, 181, 191, 12, 133, 193, 197, 199, 211

Offset: 1

Author

Rémy Sigrist, Oct 06 2023

Keywords

• nonn
• tabl

Comments

This sequence is a variant of A366030, with one less constraint.

All the prime numbers appear in the sequence, in ascending order.

For any prime number p, the first multiple of p in the sequence is p.

Will every positive integer appear in the sequence?

Examples

			Array A(n, k) begins:
  n\k |   1    2    3    4    5    6    7    8    9   10
  ----+-------------------------------------------------
    1 |   1    3    4   13   23   35   67   89  121  167
    2 |   2    7   11   15   41   61   83  127  163  199
    3 |   5    8   21   37   59   79  113  157  197  247
    4 |   9   19   31   14   55  109  151  193  221  307
    5 |  17   25   53   73    6  143  133  241  293  353
    6 |  29   47   65  107  119   12  239  283  349  401
    7 |  43   71  103  149  191  233   10   33  161  463
    8 |  49  101  139  181  229  281   27   16   95  451
    9 |  97  137  179  227  277  323  341   91   18  115
   10 | 131  173  223  253  347  397  461   85  613   24
		

Links

• Rémy Sigrist, Colored representation of the array for n, k <= 881 (grayish pixels correspond to prime numbers)
• Rémy Sigrist, PARI program

Crossrefs

Cf. A336349, A366030, A366304.

Programs

PARI

See Links section.