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A336348 Square spiral of positive integers constructed by greedy algorithm, such that for any k > 0, k appears exactly k times, and all occurrences of k lie on the same row or on the same column. 1
1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 3, 8, 8, 8, 4, 9, 9, 9, 9, 5, 10, 10, 10, 10, 6, 11, 11, 11, 11, 11, 7, 12, 12, 12, 12, 12, 8, 4, 13, 13, 13, 13, 13, 9, 5, 14, 14, 14, 14, 14, 10, 6, 15, 15, 15, 15, 15, 15, 11, 7, 16, 16, 16, 16, 16, 16, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence can be seen as a two-dimensional variant of A002024.

For symmetry reasons, we obtain the same sequence when considering a clockwise or a counterclockwise square spiral, or when initially moving towards any unit direction.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10201

Rémy Sigrist, Colored representation of the spiral for -500 <= x <= 500 and -500 <= y <= 500 (where the hue is function of a(n))

Rémy Sigrist, Colored representation of the spiral for -500 <= x <= 500 and -500 <= y <= 500 (where the hue is function of a(n) mod 4)

Rémy Sigrist, PARI program for A336348

EXAMPLE

The spiral begins:

      15--15--15--15--15--15---6--10--14

       |                               |

      11  11--11--11--11--11---6--10  14

       |   |                       |   |

       7   7   7---7---7---7---6  10  14

       |   |   |               |   |   |

      16  12   3   3---3---2   6  10  14

       |   |   |   |       |   |   |   |

      16  12   8   4   1---2   6  10  14

       |   |   |   |           |   |   |

      16  12   8   4---5---5---5   5   5

       |   |   |                   |   |

      16  12   8---4---9---9---9---9   9

       |   |                           |

      16  12---8---4--13--13--13--13--13

       |

      16--12---8--17--17--17--17--17--17

PROG

(PARI) See Links section.

CROSSREFS

Cf. A002024.

Sequence in context: A090616 A186704 A067434 * A177357 A320297 A165906

Adjacent sequences:  A336345 A336346 A336347 * A336349 A336350 A336351

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jul 19 2020

STATUS

approved

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Last modified May 16 14:39 EDT 2021. Contains 343949 sequences. (Running on oeis4.)