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A366031 Square array A(n, k), n, k >= 0, read and filled by upwards antidiagonals the greedy way with distinct nonnegative integers such that the binary expansions of any two distinct terms in the same row or column or antidiagonal have no common 1's.

%I A366031 #11 Oct 08 2023 09:00:27
%S A366031 0,1,2,4,8,16,10,17,32,64,48,68,128,256,9,192,512,257,34,20,1024,768,
%T A366031 1056,6,144,2048,4096,8192,3072,4224,520,8193,16384,320,32768,36,
%U A366031 12288,16640,1088,2052,32896,544,65536,131072,262144,49152,67584,135168,262152,258,524288,1048576,1536,8256,2097152
%N A366031 Square array A(n, k), n, k >= 0, read and filled by upwards antidiagonals the greedy way with distinct nonnegative integers such that the binary expansions of any two distinct terms in the same row or column or antidiagonal have no common 1's.
%C A366031 This sequence is a variant of A366030; here we avoid common 1's in binary expansions, there common prime factors.
%C A366031 All the powers of 2 appear in the sequence, in ascending order.
%C A366031 For any k >= 0, the first term of the sequence whose binary expansion contains 2^k is 2^k.
%C A366031 Will every nonnegative integer appear in the sequence?
%H A366031 Rémy Sigrist, <a href="/A366031/a366031.png">Colored representation of the array for n, k <= 673</a> (grayish pixels correspond to powers of 2)
%H A366031 Rémy Sigrist, <a href="/A366031/a366031.gp.txt">PARI program</a>
%e A366031 Array A(n, k) begins:
%e A366031   n\k|    1      2       3       4        5        6        7         8
%e A366031   ---+-----------------------------------------------------------------
%e A366031     1|    0      2      16      64        9     1024     8192        36
%e A366031     2|    1      8      32     256       20     4096    32768    131072
%e A366031     3|    4     17     128      34     2048      320    65536      1536
%e A366031     4|   10     68     257     144    16384      544  1048576      6144
%e A366031     5|   48    512       6    8193    32896   524288       72   4194560
%e A366031     6|  192   1056     520    2052      258  2097153    20480     32784
%e A366031     7|  768   4224    1088  262152  1048608       18     2049  67117056
%e A366031     8| 3072  16640  135168   33280    65600       12       50       129
%o A366031 (PARI) See Links section.
%Y A366031 Cf. A366030.
%K A366031 nonn,base,tabl
%O A366031 0,3
%A A366031 _Rémy Sigrist_, Sep 26 2023