A336350 -id:A336350 - cp's OEIS frontend

A336349 Square spiral of distinct positive integers constructed by greedy algorithm, such that all terms on the same row or on the same column are pairwise coprime.

1, 2, 3, 4, 5, 7, 6, 11, 13, 17, 9, 19, 8, 23, 15, 29, 31, 37, 25, 41, 12, 43, 47, 35, 53, 59, 49, 61, 67, 71, 10, 73, 79, 83, 89, 77, 27, 91, 97, 101, 95, 103, 16, 107, 109, 113, 121, 65, 51, 127, 131, 137, 139, 119, 149, 151, 18, 143, 157, 163, 133, 167, 173

Offset: 1

Rémy Sigrist, Jul 19 2020

nonn

We can always extend the sequence with a prime number greater than any previous term, so the sequence is well defined.

For symmetry reasons, we obtain the same sequence when considering a clockwise or a counterclockwise square spiral, or when initially moving towards any unit direction.

			The spiral begins:
       85--179--173--167--133--163--157--143---18
        |                                       |
      169   27---77---89---83---79---73---10  151
        |    |                             |    |
      181   91   31---29---15---23----8   71  149
        |    |    |                   |    |    |
      191   97   37    5----4----3   19   67  119
        |    |    |    |         |    |    |    |
      193  101   25    7    1----2    9   61  139
        |    |    |    |              |    |    |
      197   95   41    6---11---13---17   49  137
        |    |    |                        |    |
      199  103   12---43---47---35---53---59  131
        |    |                                  |
      161   16--107--109--113--121---65---51--127
        |
       22--211--221--223--227--229--203--233--115

Rémy Sigrist, Table of n, a(n) for n = 1..10201
Rémy Sigrist, Colored representation of the spiral for -150 < x < 150 and -150 < y < 150 (where the hue is function of a(n))
Rémy Sigrist, Colored representation of the spiral for -150 < x < 150 and -150 < y < 150 (where black pixels correspond to prime numbers)
Rémy Sigrist, PARI program for A336349

See A336350 for a similar sequence.

PARI
```
See Links section.
```

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
```
See Links section.
```

cp's OEIS Frontend

A336349 Square spiral of distinct positive integers constructed by greedy algorithm, such that all terms on the same row or on the same column are pairwise coprime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI