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

Author

Rémy Sigrist, Jul 19 2020

Keywords

• nonn

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.

Examples

			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
		

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

Crossrefs

See A336350 for a similar sequence.

Programs

PARI

See Links section.