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

0,4

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).

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A307838 for the multiplicative variant.

Cf A174344, A274923.

Sequence in context: A274847 A165922 A337293 * A326616 A249033 A068762

Adjacent sequences: A307831 A307832 A307833 * A307835 A307836 A307837

Keyword

nonn,look

Author

Rémy Sigrist, May 01 2019

Status

approved