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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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).

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

EXAMPLE

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

PROG

(PARI) See Links section.

CROSSREFS

See A307834 for the additive variant.

Cf. A088177.

Sequence in context: A269526 A106448 A295280 * A159909 A176004 A214738

Adjacent sequences:  A307835 A307836 A307837 * A307839 A307840 A307841

KEYWORD

nonn

AUTHOR

Rémy Sigrist, May 01 2019

STATUS

approved

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Last modified August 12 04:57 EDT 2020. Contains 336436 sequences. (Running on oeis4.)