A307838 Counterclockwise square spiral constructed by greedy algorithm such that the product of the values of any two vertically or horizontally adjacent cells is unique.

1, 1, 2, 3, 3, 4, 2, 5, 7, 2, 11, 8, 3, 9, 5, 10, 2, 13, 7, 16, 3, 17, 5, 8, 18, 3, 19, 4, 13, 11, 5, 14, 7, 12, 8, 23, 1, 29, 5, 15, 8, 22, 5, 23, 4, 18, 17, 6, 26, 5, 27, 6, 25, 9, 11, 19, 1, 31, 9, 17, 11, 20, 7, 21, 8, 37, 3, 41, 11, 24, 9, 35, 6, 34, 10

Offset: 0

Author

Rémy Sigrist, May 01 2019

Keywords

• nonn

Comments

This sequence is a two-dimensional variant of A088177.

Visually, we have a superposition of two images that we can separate by considering the parity of the sum of the x and y coordinates (see illustrations in Links section).

Examples

			The spiral begins:
    7---19---16---29---14---22---13---43----3---47----2
    |                                                 |
   31    8---21----7---20---11---17----9---31----1   43
    |    |                                       |    |
    2   37    1---23----8---12----7---14----5   19   14
    |    |    |                             |    |    |
   53    3   29    2---10----5----9----3   11   11   14
    |    |    |    |                   |    |    |    |
    4   41    5   13    3----3----2    8   13    9   21
    |    |    |    |    |         |    |    |    |    |
   37   11   15    7    4    1----1   11    4   25   11
    |    |    |    |    |              |    |    |    |
   10   24    8   16    2----5----7----2   19    6   31
    |    |    |    |                        |    |    |
   19    9   22    3---17----5----8---18----3   27   10
    |    |    |                                  |    |
   12   35    5---23----4---18---17----6---26----5   25
    |    |                                            |
   23    6---34---10---29---13----1---41----7---36----8
    |
    9---29----8---26---12---25---49----8---32---10---43
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10200 (-50 <= x <= 50 and -50 <= y <= 50)
• Rémy Sigrist, Colored illustration of the sequence (with cells (x,y) such that -500 <= x <= 500 and -500 <= y <= 500)
• Rémy Sigrist, Colored illustration of the sequence in function of the parities of x and y
• Rémy Sigrist, PARI program for A307838

Crossrefs

See A307834 for the additive variant.

Cf. A088177.

Programs

PARI

See Links section.