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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.

%I A366030 #13 Oct 08 2023 08:58:45
%S A366030 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,
%T A366030 61,67,49,71,55,73,57,79,83,89,97,77,101,103,107,16,109,113,65,127,
%U A366030 131,137,85,139,91,121,149,151,157,163,167,169,173,179,181,6,115,119,191,193,197
%N 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.
%C A366030 This sequence is a variant of A284145 (with one less constraint).
%C A366030 All the prime numbers appear in the sequence, in ascending order.
%C A366030 For any prime number p, the first multiple of p in the sequence is p.
%C A366030 Will every positive integer appear in the sequence?
%H A366030 Rémy Sigrist, <a href="/A366030/a366030.png">Colored representation of the array for n, k <= 500</a> (grayish pixels correspond to prime numbers)
%H A366030 Rémy Sigrist, <a href="/A366030/a366030.gp.txt">PARI program</a>
%e A366030 Array A(n, k) begins:
%e A366030   n\k|   1    2    3    4    5    6    7    8    9   10
%e A366030   ---+-------------------------------------------------
%e A366030     1|   1    3    4   13   25   43   49   97  127  163
%e A366030     2|   2    7   11   23   27   67   89   65  157  193
%e A366030     3|   5    8   21   41   61   83  113  151  191  221
%e A366030     4|   9   19   37   10   79  109  149  119  239  281
%e A366030     5|  17   31   59   57   16  121  115  233  203  347
%e A366030     6|  29   53   73  107   91    6  229  277  337  125
%e A366030     7|  47   55  103  139  181  161   12  331  323  463
%e A366030     8|  71  101   85  179  209  271  317   18  403  259
%e A366030     9|  77  137  173  227  269   95  377  461   24  613
%e A366030    10| 131  169  223  187  313  397  457  437  185   32
%o A366030 (PARI) See Links section.
%Y A366030 Cf. A284145, A366031, A366303.
%K A366030 nonn,tabl
%O A366030 1,2
%A A366030 _Rémy Sigrist_, Sep 26 2023