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

%I A360633 #12 Feb 25 2023 15:28:31
%S A360633 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,
%T A360633 30,17,18,42,65,72,77,60,34,19,23,54,70,104,99,105,68,38,24,25,69,90,
%U A360633 112,143,135,119,76,48,29,26,75,115,144,154,195,153,133,96,58,31
%N A360633 Square array A(n, k), n, k > 0, read by antidiagonals upwards; A(n, k) = A360613(2*n-1) * A360613(2*k).
%C A360633 This sequence can be seen as a greedy multiplication table where we alternately add rows and columns so that all products are distinct.
%C A360633 Conjecture: all integers appear in this sequence.
%H A360633 Rémy Sigrist, <a href="/A360633/b360633.txt">Table of n, a(n) for n = 1..10011</a>
%H A360633 Rémy Sigrist, <a href="/A360633/a360633.txt">C program</a>
%F A360633 A(n, k) = A360627(n) * A360628(k).
%F A360633 A(n, 1) = A360627(n).
%F A360633 A(1, k) = A360628(k).
%e A360633 Array A(n, k) begins:
%e A360633   n\k |  1   2    3    4    5    6    7    8    9   10
%e A360633   ----+-----------------------------------------------
%e A360633     1 |  1   3    5    8   11   15   17   19   24   29
%e A360633     2 |  2   6   10   16   22   30   34   38   48   58
%e A360633     3 |  4  12   20   32   44   60   68   76   96  116
%e A360633     4 |  7  21   35   56   77  105  119  133  168  203
%e A360633     5 |  9  27   45   72   99  135  153  171  216  261
%e A360633     6 | 13  39   65  104  143  195  221  247  312  377
%e A360633     7 | 14  42   70  112  154  210  238  266  336  406
%e A360633     8 | 18  54   90  144  198  270  306  342  432  522
%e A360633     9 | 23  69  115  184  253  345  391  437  552  667
%e A360633    10 | 25  75  125  200  275  375  425  475  600  725
%o A360633 (C) See Links section.
%Y A360633 Cf. A249327, A360613, A360627, A360628.
%K A360633 nonn,tabl
%O A360633 1,2
%A A360633 _Rémy Sigrist_, Feb 14 2023