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A274917 Square spiral in which each new term is the least positive integer distinct from its (already assigned) eight neighbors. 3
1, 2, 3, 4, 2, 3, 2, 4, 3, 1, 4, 1, 2, 5, 1, 3, 1, 4, 1, 4, 1, 3, 1, 2, 4, 2, 3, 2, 3, 4, 1, 3, 4, 2, 4, 2, 3, 5, 2, 3, 2, 3, 2, 4, 2, 4, 3, 1, 3, 1, 4, 1, 4, 1, 2, 3, 2, 4, 2, 1, 3, 1, 5, 1, 2, 4, 1, 4, 1, 4, 1, 4, 1, 3, 1, 3, 1, 2, 4, 2, 4, 2, 3, 2, 3, 2, 3, 4, 1, 4, 1, 3, 1, 3, 4, 2, 4, 2, 3, 4, 1, 3, 5, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The largest element is 5 and it is also the element with lower density in the spiral.

See A275609 for proof that 5 is maximal and for further comments. - N. J. A. Sloane, Mar 24 2019

LINKS

Table of n, a(n) for n=0..104.

F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.

FORMULA

a(n) = A275609(n) + 1. - Omar E. Pol, Nov 14 2016

EXAMPLE

Illustration of initial terms as a spiral (n = 0..168):

.

.     2 - 3 - 2 - 1 - 5 - 1 - 3 - 1 - 2 - 4 - 2 - 4 - 2

.     |                                               |

.     4   1 - 4 - 3 - 2 - 4 - 2 - 4 - 3 - 1 - 3 - 1   3

.     |   |                                       |   |

.     2   3   2 - 1 - 5 - 1 - 3 - 1 - 2 - 4 - 2   4   2

.     |   |   |                               |   |   |

.     1   5   4   3 - 2 - 4 - 2 - 4 - 3 - 1   3   1   3

.     |   |   |   |                       |   |   |   |

.     4   2   1   5   1 - 3 - 1 - 5 - 2   4   2   4   2

.     |   |   |   |   |               |   |   |   |   |

.     1   3   4   2   4   2 - 4 - 3   1   3   1   3   1

.     |   |   |   |   |   |       |   |   |   |   |   |

.     4   2   1   3   1   3   1 - 2   4   2   4   2   4

.     |   |   |   |   |   |           |   |   |   |   |

.     1   3   4   2   4   2 - 4 - 3 - 1   3   1   3   1

.     |   |   |   |   |                   |   |   |   |

.     4   2   1   3   1 - 3 - 1 - 2 - 4 - 2   4   2   4

.     |   |   |   |                           |   |   |

.     1   3   4   2 - 4 - 2 - 4 - 3 - 1 - 3 - 1   3   1

.     |   |   |                                   |   |

.     4   2   1 - 3 - 1 - 3 - 1 - 2 - 4 - 2 - 4 - 2   4

.     |   |                                           |

.     1   3 - 4 - 2 - 4 - 2 - 4 - 3 - 1 - 3 - 1 - 3 - 1

.     |

.     2 - 5 - 1 - 3 - 1 - 3 - 1 - 2 - 4 - 2 - 4 - 2 - 4

.

a(13) = 5 is the first "5" in the sequence and its four neighbors are 4 (southwest), 3 (south), 1 (southeast) and 2 (east) when a(13) is placed in the spiral.

a(157) = 5 is the 6th "5" in the sequence and it is also the first "5" that is below the NE-SW main diagonal of the spiral (see the second term in the last row of the above diagram).

CROSSREFS

Cf. A274913, A274921, A275609, A278354 (number of neighbors).

Sequence in context: A256445 A275103 A107795 * A302795 A272726 A262304

Adjacent sequences:  A274914 A274915 A274916 * A274918 A274919 A274920

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jul 11 2016

STATUS

approved

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Last modified May 25 02:01 EDT 2020. Contains 334581 sequences. (Running on oeis4.)