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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 16 15:53 EST 2021. Contains 340206 sequences. (Running on oeis4.)