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A307838 Counterclockwise square spiral constructed by greedy algorithm such that the product of the values of any two vertically or horizontally adjacent cells is unique.

%I A307838 #14 May 01 2019 17:25:36
%S A307838 1,1,2,3,3,4,2,5,7,2,11,8,3,9,5,10,2,13,7,16,3,17,5,8,18,3,19,4,13,11,
%T A307838 5,14,7,12,8,23,1,29,5,15,8,22,5,23,4,18,17,6,26,5,27,6,25,9,11,19,1,
%U A307838 31,9,17,11,20,7,21,8,37,3,41,11,24,9,35,6,34,10
%N A307838 Counterclockwise square spiral constructed by greedy algorithm such that the product of the values of any two vertically or horizontally adjacent cells is unique.
%C A307838 This sequence is a two-dimensional variant of A088177.
%C A307838 Visually, we have a superposition of two images that we can separate by considering the parity of the sum of the x and y coordinates (see illustrations in Links section).
%H A307838 Rémy Sigrist, <a href="/A307838/b307838.txt">Table of n, a(n) for n = 0..10200</a> (-50 <= x <= 50 and -50 <= y <= 50)
%H A307838 Rémy Sigrist, <a href="/A307838/a307838.png">Colored illustration of the sequence (with cells (x,y) such that -500 <= x <= 500 and -500 <= y <= 500)</a>
%H A307838 Rémy Sigrist, <a href="/A307838/a307838_1.png">Colored illustration of the sequence in function of the parities of x and y</a>
%H A307838 Rémy Sigrist, <a href="/A307838/a307838.gp.txt">PARI program for A307838</a>
%e A307838 The spiral begins:
%e A307838     7---19---16---29---14---22---13---43----3---47----2
%e A307838     |                                                 |
%e A307838    31    8---21----7---20---11---17----9---31----1   43
%e A307838     |    |                                       |    |
%e A307838     2   37    1---23----8---12----7---14----5   19   14
%e A307838     |    |    |                             |    |    |
%e A307838    53    3   29    2---10----5----9----3   11   11   14
%e A307838     |    |    |    |                   |    |    |    |
%e A307838     4   41    5   13    3----3----2    8   13    9   21
%e A307838     |    |    |    |    |         |    |    |    |    |
%e A307838    37   11   15    7    4    1----1   11    4   25   11
%e A307838     |    |    |    |    |              |    |    |    |
%e A307838    10   24    8   16    2----5----7----2   19    6   31
%e A307838     |    |    |    |                        |    |    |
%e A307838    19    9   22    3---17----5----8---18----3   27   10
%e A307838     |    |    |                                  |    |
%e A307838    12   35    5---23----4---18---17----6---26----5   25
%e A307838     |    |                                            |
%e A307838    23    6---34---10---29---13----1---41----7---36----8
%e A307838     |
%e A307838     9---29----8---26---12---25---49----8---32---10---43
%o A307838 (PARI) See Links section.
%Y A307838 See A307834 for the additive variant.
%Y A307838 Cf. A088177.
%K A307838 nonn
%O A307838 0,3
%A A307838 _Rémy Sigrist_, May 01 2019