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%I #14 May 01 2019 17:25:36
%S 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 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 31,9,17,11,20,7,21,8,37,3,41,11,24,9,35,6,34,10
%N 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 This sequence is a two-dimensional variant of A088177.
%C 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 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 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 Rémy Sigrist, <a href="/A307838/a307838_1.png">Colored illustration of the sequence in function of the parities of x and y</a>
%H Rémy Sigrist, <a href="/A307838/a307838.gp.txt">PARI program for A307838</a>
%e The spiral begins:
%e 7---19---16---29---14---22---13---43----3---47----2
%e | |
%e 31 8---21----7---20---11---17----9---31----1 43
%e | | | |
%e 2 37 1---23----8---12----7---14----5 19 14
%e | | | | | |
%e 53 3 29 2---10----5----9----3 11 11 14
%e | | | | | | | |
%e 4 41 5 13 3----3----2 8 13 9 21
%e | | | | | | | | | |
%e 37 11 15 7 4 1----1 11 4 25 11
%e | | | | | | | | |
%e 10 24 8 16 2----5----7----2 19 6 31
%e | | | | | | |
%e 19 9 22 3---17----5----8---18----3 27 10
%e | | | | |
%e 12 35 5---23----4---18---17----6---26----5 25
%e | | |
%e 23 6---34---10---29---13----1---41----7---36----8
%e |
%e 9---29----8---26---12---25---49----8---32---10---43
%o (PARI) See Links section.
%Y See A307834 for the additive variant.
%Y Cf. A088177.
%K nonn
%O 0,3
%A _Rémy Sigrist_, May 01 2019
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