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

1,2

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?

Links

Table of n, a(n) for n=1..66.

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

Rémy Sigrist, PARI program

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A336349, A366030, A366304.

Sequence in context: A082331 A140528 A065037 * A366030 A101438 A103683

Adjacent sequences: A366300 A366301 A366302 * A366304 A366305 A366306

Keyword

nonn,tabl

Author

Rémy Sigrist, Oct 06 2023

Status

approved