A366030 -id:A366030 - cp's OEIS frontend

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

Rémy Sigrist, Sep 26 2023

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?

			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

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

Cf. A366030.

PARI
```
See Links section.
```

A366303 Square array A(n, k), n, k > 0, read and filled by upwards antidiagonals the greedy way with distinct positive integers such that any two distinct terms in the same row or column are coprime.

Original entry on oeis.org

1, 2, 3, 5, 7, 4, 9, 8, 11, 13, 17, 19, 21, 15, 23, 29, 25, 31, 37, 41, 35, 43, 47, 53, 14, 59, 61, 67, 49, 71, 65, 73, 55, 79, 83, 89, 97, 101, 103, 107, 6, 109, 113, 127, 121, 131, 137, 139, 149, 119, 143, 151, 157, 163, 167, 169, 173, 179, 181, 191, 12, 133, 193, 197, 199, 211

Offset: 1

Rémy Sigrist, Oct 06 2023

This sequence is a variant of A366030, with one less constraint.
All the prime numbers appear in the sequence, in ascending order.
For any prime number p, the first multiple of p in the sequence is p.
Will every positive integer appear in the sequence?

			Array A(n, k) begins:
  n\k |   1    2    3    4    5    6    7    8    9   10
  ----+-------------------------------------------------
    1 |   1    3    4   13   23   35   67   89  121  167
    2 |   2    7   11   15   41   61   83  127  163  199
    3 |   5    8   21   37   59   79  113  157  197  247
    4 |   9   19   31   14   55  109  151  193  221  307
    5 |  17   25   53   73    6  143  133  241  293  353
    6 |  29   47   65  107  119   12  239  283  349  401
    7 |  43   71  103  149  191  233   10   33  161  463
    8 |  49  101  139  181  229  281   27   16   95  451
    9 |  97  137  179  227  277  323  341   91   18  115
   10 | 131  173  223  253  347  397  461   85  613   24

Rémy Sigrist, Colored representation of the array for n, k <= 881 (grayish pixels correspond to prime numbers)
Rémy Sigrist, PARI program

Cf. A336349, A366030, A366304.

PARI
```
See Links section.
```

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI