A307834 Counterclockwise square spiral constructed by greedy algorithm such that the sum of the values of any two vertically or horizontally adjacent cells is unique.

0, 0, 1, 2, 2, 5, 1, 8, 10, 1, 12, 13, 2, 15, 17, 18, 3, 20, 19, 25, 2, 27, 22, 21, 32, 2, 35, 26, 28, 38, 4, 43, 31, 31, 32, 48, 4, 52, 37, 39, 34, 58, 6, 63, 40, 46, 49, 39, 70, 5, 76, 42, 56, 51, 45, 80, 5, 86, 44, 62, 66, 67, 46, 96, 5, 100, 50, 71, 72, 76

Offset: 0

Author

Rémy Sigrist, May 01 2019

Keywords

• nonn
• look

Comments

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:
    8--158---69--111---91---95---93--110---61--147----6
    |                                                 |
  164    5---96---46---67---66---62---44---86----5  140
    |    |                                       |    |
   67  100    4---48---32---31---31---43----4   80   64
    |    |    |                             |    |    |
  123   50   52    3---18---17---15----2   38   45   96
    |    |    |    |                   |    |    |    |
   97   71   37   20    2----2----1   13   28   51   88
    |    |    |    |    |         |    |    |    |    |
  102   72   39   19    5    0----0   12   26   56   82
    |    |    |    |    |              |    |    |    |
   99   76   34   25    1----8---10----1   35   42   94
    |    |    |    |                        |    |    |
  123   56   58    2---27---22---21---32----2   76   55
    |    |    |                                  |    |
   71  106    6---63---40---46---49---39---70----5  130
    |    |                                            |
  172    9--110---54---80---76---75---84---56--122----7
    |
   10--182---73--133--109--117--120--112--141---76--193
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10200 (-50 <= x <= 50 and -50 <= y <= 50)
• Peter Kagey and Rémy Sigrist, Colored representation of z(2*k)/abs(z(2*k))*a(2*k) for k = 1..501000 (where z(n) = A174344(n) + i*A274923(n) and the hue is function of k)
• Peter Kagey and Rémy Sigrist, Colored representation of z(2*k-1)/abs(z(2*k-1))*a(2*k-1) for k = 1..501000 (where z(n) = A174344(n) + i*A274923(n) and the hue is function of k)
• 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 A307834

Crossrefs

See A307838 for the multiplicative variant.

Cf A174344, A274923.

Programs

PARI

See Links section.