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%I #5 Oct 08 2023 09:01:13
%S 0,1,2,4,8,5,10,16,18,24,32,33,40,36,64,80,68,128,3,256,160,384,512,
%T 768,320,640,576,1024,1536,2048,3072,1152,20,1280,2176,2304,4096,4224,
%U 4160,8192,9,6144,8256,5120,4608,10240,8448,16384,16896,34,8194,32768,49152,24576,40960
%N 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 This sequence is a variant of A366031, with one less constraint.
%C All the powers of 2 appear in the sequence, in ascending order.
%C For any k >= 0, the first term of the sequence whose binary expansion contains 2^k is 2^k.
%C Will every nonnegative integer appear in the sequence?
%H 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 Rémy Sigrist, <a href="/A366304/a366304.gp.txt">PARI program</a>
%e Array A(n, k) begins:
%e n\k | 0 1 2 3 4 5 6 7
%e ----+-----------------------------------------------------------------
%e 0 | 0 2 5 24 64 160 1024 2304
%e 1 | 1 8 18 36 256 576 2176 5120
%e 2 | 4 16 40 3 640 1280 8256 49152
%e 3 | 10 33 128 320 20 6144 32768 8704
%e 4 | 32 68 768 1152 9 8194 4112 327680
%e 5 | 80 512 3072 8192 34 12 257 131200
%e 6 | 384 2048 4160 16896 9216 17 6 524296
%e 7 | 1536 4224 16384 34816 196608 786432 1048584 7
%e 8 | 4096 8448 98304 393216 18432 5242880 544 2097168
%e 9 | 10240 17408 262144 69632 1081344 2228224 4718592 96
%o (PARI) See Links section.
%Y Cf. A336350, A366031.
%K nonn,base,tabl
%O 0,3
%A _Rémy Sigrist_, Oct 06 2023