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A336349 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.

%I A336349 #13 Jul 25 2020 12:29:36
%S A336349 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 A336349 49,61,67,71,10,73,79,83,89,77,27,91,97,101,95,103,16,107,109,113,121,
%U A336349 65,51,127,131,137,139,119,149,151,18,143,157,163,133,167,173
%N A336349 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 A336349 We can always extend the sequence with a prime number greater than any previous term, so the sequence is well defined.
%C A336349 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 A336349 Rémy Sigrist, <a href="/A336349/b336349.txt">Table of n, a(n) for n = 1..10201</a>
%H A336349 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 A336349 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 A336349 Rémy Sigrist, <a href="/A336349/a336349.gp.txt">PARI program for A336349</a>
%e A336349 The spiral begins:
%e A336349        85--179--173--167--133--163--157--143---18
%e A336349         |                                       |
%e A336349       169   27---77---89---83---79---73---10  151
%e A336349         |    |                             |    |
%e A336349       181   91   31---29---15---23----8   71  149
%e A336349         |    |    |                   |    |    |
%e A336349       191   97   37    5----4----3   19   67  119
%e A336349         |    |    |    |         |    |    |    |
%e A336349       193  101   25    7    1----2    9   61  139
%e A336349         |    |    |    |              |    |    |
%e A336349       197   95   41    6---11---13---17   49  137
%e A336349         |    |    |                        |    |
%e A336349       199  103   12---43---47---35---53---59  131
%e A336349         |    |                                  |
%e A336349       161   16--107--109--113--121---65---51--127
%e A336349         |
%e A336349        22--211--221--223--227--229--203--233--115
%o A336349 (PARI) See Links section.
%Y A336349 See A336350 for a similar sequence.
%K A336349 nonn
%O A336349 1,2
%A A336349 _Rémy Sigrist_, Jul 19 2020