A366030 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 or antidiagonal are coprime.

1, 2, 3, 5, 7, 4, 9, 8, 11, 13, 17, 19, 21, 23, 25, 29, 31, 37, 41, 27, 43, 47, 53, 59, 10, 61, 67, 49, 71, 55, 73, 57, 79, 83, 89, 97, 77, 101, 103, 107, 16, 109, 113, 65, 127, 131, 137, 85, 139, 91, 121, 149, 151, 157, 163, 167, 169, 173, 179, 181, 6, 115, 119, 191, 193, 197

Offset

1,2

Comments

This sequence is a variant of A284145 (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 <= 500 (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   25   43   49   97  127  163
    2|   2    7   11   23   27   67   89   65  157  193
    3|   5    8   21   41   61   83  113  151  191  221
    4|   9   19   37   10   79  109  149  119  239  281
    5|  17   31   59   57   16  121  115  233  203  347
    6|  29   53   73  107   91    6  229  277  337  125
    7|  47   55  103  139  181  161   12  331  323  463
    8|  71  101   85  179  209  271  317   18  403  259
    9|  77  137  173  227  269   95  377  461   24  613
   10| 131  169  223  187  313  397  457  437  185   32

Prog

(PARI) See Links section.

Crossrefs

Cf. A284145, A366031, A366303.

Sequence in context: A140528 A065037 A366303 * A101438 A103683 A356903

Adjacent sequences: A366027 A366028 A366029 * A366031 A366032 A366033

Keyword

nonn,tabl

Author

Rémy Sigrist, Sep 26 2023

Status

approved