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.

0, 1, 2, 4, 8, 16, 10, 17, 32, 64, 48, 68, 128, 256, 9, 192, 512, 257, 34, 20, 1024, 768, 1056, 6, 144, 2048, 4096, 8192, 3072, 4224, 520, 8193, 16384, 320, 32768, 36, 12288, 16640, 1088, 2052, 32896, 544, 65536, 131072, 262144, 49152, 67584, 135168, 262152, 258, 524288, 1048576, 1536, 8256, 2097152

Offset: 0

Author

Rémy Sigrist, Sep 26 2023

Keywords

• nonn
• base
• tabl

Comments

This sequence is a variant of A366030; here we avoid common 1's in binary expansions, there common prime factors.

All the powers of 2 appear in the sequence, in ascending order.

For any k >= 0, the first term of the sequence whose binary expansion contains 2^k is 2^k.

Will every nonnegative integer appear in the sequence?

Examples

			Array A(n, k) begins:
  n\k|    1      2       3       4        5        6        7         8
  ---+-----------------------------------------------------------------
    1|    0      2      16      64        9     1024     8192        36
    2|    1      8      32     256       20     4096    32768    131072
    3|    4     17     128      34     2048      320    65536      1536
    4|   10     68     257     144    16384      544  1048576      6144
    5|   48    512       6    8193    32896   524288       72   4194560
    6|  192   1056     520    2052      258  2097153    20480     32784
    7|  768   4224    1088  262152  1048608       18     2049  67117056
    8| 3072  16640  135168   33280    65600       12       50       129
		

Links

• Rémy Sigrist, Colored representation of the array for n, k <= 673 (grayish pixels correspond to powers of 2)
• Rémy Sigrist, PARI program

Crossrefs

Cf. A366030.

Programs

PARI

See Links section.