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A308505 Counterclockwise square spiral of distinct positive integers constructed by greedy algorithm, such that for p = 2 and 3, every multiple of p (except p itself) is vertically or horizontally adjacent to a cell already holding a multiple of p. 2
1, 2, 3, 5, 7, 11, 13, 17, 4, 8, 10, 6, 9, 15, 19, 23, 25, 29, 31, 35, 37, 41, 43, 14, 16, 20, 22, 26, 12, 18, 21, 27, 33, 39, 45, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 77, 28, 32, 34, 38, 40, 44, 46, 24, 30, 36, 42, 48, 50, 51, 57, 63, 69, 75, 79, 83, 85 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For p = 2 and 3, the set S_p of lattice points holding a multiple of p is connected with respect to von Neumann neighborhood and has interesting graphical features (see representation in Links section).

Apparently this sequence is a permutation of the natural number with infinitely many fixed points.

LINKS

Table of n, a(n) for n=1..67.

Rémy Sigrist, Representation of S_2 restricted to -500 <= x <= +500 and -500 <= y <= +500

Rémy Sigrist, Representation of S_3 restricted to -500 <= x <= +500 and -500 <= y <= +500

Rémy Sigrist, Colored representation of (a(n)-n) restricted to -500 <= x <= +500 and -500 <= y <= +500 (where black pixels correspond to zeros, blue shades correspond to negative values and red shades correspond to positive values)

Rémy Sigrist, PARI program for A308505

EXAMPLE

The spiral begins:

  111--105---99---93---87---86---84---82---81---80---78

    |                                                 |

  117   79---75---69---63---57---51---50---48---42   72

    |    |                                       |    |

  119   83   49---47---45---39---33---27---21   36   66

    |    |    |                             |    |    |

  121   85   53   25---23---19---15----9   18   30   60

    |    |    |    |                   |    |    |    |

  125   89   55   29    7----5----3    6   12   24   54

    |    |    |    |    |         |    |    |    |    |

  127   91   59   31   11    1----2   10   26   46   76

    |    |    |    |    |              |    |    |    |

  131   95   61   35   13---17----4----8   22   44   74

    |    |    |    |                        |    |    |

  133   97   65   37---41---43---14---16---20   40   70

    |    |    |                                  |    |

  137  101   67---71---73---77---28---32---34---38   68

    |    |                                            |

  139  103--107--109--113--115---52---56---58---62---64

    |

  143--145--149--151--155--157---88---92---94---98--100

PROG

(PARI) See Links section.

CROSSREFS

Cf. A005843, A008585.

Sequence in context: A020625 A033633 A242119 * A249823 A171049 A171053

Adjacent sequences:  A308502 A308503 A308504 * A308506 A308507 A308508

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jun 02 2019

STATUS

approved

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Last modified April 9 09:35 EDT 2020. Contains 333344 sequences. (Running on oeis4.)