A366031 -id:A366031 - cp's OEIS frontend

A366030 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 or antidiagonal are coprime.

1, 2, 3, 5, 7, 4, 9, 8, 11, 13, 17, 19, 21, 23, 25, 29, 31, 37, 41, 27, 43, 47, 53, 59, 10, 61, 67, 49, 71, 55, 73, 57, 79, 83, 89, 97, 77, 101, 103, 107, 16, 109, 113, 65, 127, 131, 137, 85, 139, 91, 121, 149, 151, 157, 163, 167, 169, 173, 179, 181, 6, 115, 119, 191, 193, 197

Offset: 1

Rémy Sigrist, Sep 26 2023

This sequence is a variant of A284145 (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   25   43   49   97  127  163
    2|   2    7   11   23   27   67   89   65  157  193
    3|   5    8   21   41   61   83  113  151  191  221
    4|   9   19   37   10   79  109  149  119  239  281
    5|  17   31   59   57   16  121  115  233  203  347
    6|  29   53   73  107   91    6  229  277  337  125
    7|  47   55  103  139  181  161   12  331  323  463
    8|  71  101   85  179  209  271  317   18  403  259
    9|  77  137  173  227  269   95  377  461   24  613
   10| 131  169  223  187  313  397  457  437  185   32

Rémy Sigrist, Colored representation of the array for n, k <= 500 (grayish pixels correspond to prime numbers)
Rémy Sigrist, PARI program

Cf. A284145, A366031, A366303.

PARI
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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.

Original entry on oeis.org

0, 1, 2, 4, 8, 5, 10, 16, 18, 24, 32, 33, 40, 36, 64, 80, 68, 128, 3, 256, 160, 384, 512, 768, 320, 640, 576, 1024, 1536, 2048, 3072, 1152, 20, 1280, 2176, 2304, 4096, 4224, 4160, 8192, 9, 6144, 8256, 5120, 4608, 10240, 8448, 16384, 16896, 34, 8194, 32768, 49152, 24576, 40960

Offset: 0

Rémy Sigrist, Oct 06 2023

This sequence is a variant of A366031, with one less constraint.
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 |     0      1       2       3        4        5        6        7
  ----+-----------------------------------------------------------------
    0 |     0      2       5      24       64      160     1024     2304
    1 |     1      8      18      36      256      576     2176     5120
    2 |     4     16      40       3      640     1280     8256    49152
    3 |    10     33     128     320       20     6144    32768     8704
    4 |    32     68     768    1152        9     8194     4112   327680
    5 |    80    512    3072    8192       34       12      257   131200
    6 |   384   2048    4160   16896     9216       17        6   524296
    7 |  1536   4224   16384   34816   196608   786432  1048584        7
    8 |  4096   8448   98304  393216    18432  5242880      544  2097168
    9 | 10240  17408  262144   69632  1081344  2228224  4718592       96

Rémy Sigrist, Colored representation of the array for n, k <= 666 (grayish pixels correspond to powers of 2)
Rémy Sigrist, PARI program

Cf. A336350, A366031.

PARI
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See Links section.
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cp's OEIS Frontend

A366030 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 or antidiagonal are coprime.

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