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

1,2

Comments

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.

Links

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A336350 for a similar sequence.

Sequence in context: A080688 A082025 A076034 * A255545 A034152 A344316

Adjacent sequences: A336346 A336347 A336348 * A336350 A336351 A336352

Keyword

nonn

Author

Rémy Sigrist, Jul 19 2020

Status

approved