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A366304 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 have no common 1's.

%I A366304 #5 Oct 08 2023 09:01:13
%S A366304 0,1,2,4,8,5,10,16,18,24,32,33,40,36,64,80,68,128,3,256,160,384,512,
%T A366304 768,320,640,576,1024,1536,2048,3072,1152,20,1280,2176,2304,4096,4224,
%U A366304 4160,8192,9,6144,8256,5120,4608,10240,8448,16384,16896,34,8194,32768,49152,24576,40960
%N A366304 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 have no common 1's.
%C A366304 This sequence is a variant of A366031, with one less constraint.
%C A366304 All the powers of 2 appear in the sequence, in ascending order.
%C A366304 For any k >= 0, the first term of the sequence whose binary expansion contains 2^k is 2^k.
%C A366304 Will every nonnegative integer appear in the sequence?
%H A366304 Rémy Sigrist, <a href="/A366304/a366304.png">Colored representation of the array for n, k <= 666</a> (grayish pixels correspond to powers of 2)
%H A366304 Rémy Sigrist, <a href="/A366304/a366304.gp.txt">PARI program</a>
%e A366304 Array A(n, k) begins:
%e A366304   n\k |     0      1       2       3        4        5        6        7
%e A366304   ----+-----------------------------------------------------------------
%e A366304     0 |     0      2       5      24       64      160     1024     2304
%e A366304     1 |     1      8      18      36      256      576     2176     5120
%e A366304     2 |     4     16      40       3      640     1280     8256    49152
%e A366304     3 |    10     33     128     320       20     6144    32768     8704
%e A366304     4 |    32     68     768    1152        9     8194     4112   327680
%e A366304     5 |    80    512    3072    8192       34       12      257   131200
%e A366304     6 |   384   2048    4160   16896     9216       17        6   524296
%e A366304     7 |  1536   4224   16384   34816   196608   786432  1048584        7
%e A366304     8 |  4096   8448   98304  393216    18432  5242880      544  2097168
%e A366304     9 | 10240  17408  262144   69632  1081344  2228224  4718592       96
%o A366304 (PARI) See Links section.
%Y A366304 Cf. A336350, A366031.
%K A366304 nonn,base,tabl
%O A366304 0,3
%A A366304 _Rémy Sigrist_, Oct 06 2023