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Square spiral of distinct positive integers constructed by greedy algorithm, such that all terms on the same row or on the same column are pairwise coprime.
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%I #13 Jul 25 2020 12:29:36

%S 1,2,3,4,5,7,6,11,13,17,9,19,8,23,15,29,31,37,25,41,12,43,47,35,53,59,

%T 49,61,67,71,10,73,79,83,89,77,27,91,97,101,95,103,16,107,109,113,121,

%U 65,51,127,131,137,139,119,149,151,18,143,157,163,133,167,173

%N Square spiral of distinct positive integers constructed by greedy algorithm, such that all terms on the same row or on the same column are pairwise coprime.

%C We can always extend the sequence with a prime number greater than any previous term, so the sequence is well defined.

%C 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.

%H Rémy Sigrist, <a href="/A336349/b336349.txt">Table of n, a(n) for n = 1..10201</a>

%H Rémy Sigrist, <a href="/A336349/a336349.png">Colored representation of the spiral for -150 < x < 150 and -150 < y < 150</a> (where the hue is function of a(n))

%H Rémy Sigrist, <a href="/A336349/a336349_1.png">Colored representation of the spiral for -150 < x < 150 and -150 < y < 150</a> (where black pixels correspond to prime numbers)

%H Rémy Sigrist, <a href="/A336349/a336349.gp.txt">PARI program for A336349</a>

%e The spiral begins:

%e 85--179--173--167--133--163--157--143---18

%e | |

%e 169 27---77---89---83---79---73---10 151

%e | | | |

%e 181 91 31---29---15---23----8 71 149

%e | | | | | |

%e 191 97 37 5----4----3 19 67 119

%e | | | | | | | |

%e 193 101 25 7 1----2 9 61 139

%e | | | | | | |

%e 197 95 41 6---11---13---17 49 137

%e | | | | |

%e 199 103 12---43---47---35---53---59 131

%e | | |

%e 161 16--107--109--113--121---65---51--127

%e |

%e 22--211--221--223--227--229--203--233--115

%o (PARI) See Links section.

%Y See A336350 for a similar sequence.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jul 19 2020