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A307834 Counterclockwise square spiral constructed by greedy algorithm such that the sum of the values of any two vertically or horizontally adjacent cells is unique.

%I A307834 #23 Jun 18 2019 11:57:23
%S A307834 0,0,1,2,2,5,1,8,10,1,12,13,2,15,17,18,3,20,19,25,2,27,22,21,32,2,35,
%T A307834 26,28,38,4,43,31,31,32,48,4,52,37,39,34,58,6,63,40,46,49,39,70,5,76,
%U A307834 42,56,51,45,80,5,86,44,62,66,67,46,96,5,100,50,71,72,76
%N A307834 Counterclockwise square spiral constructed by greedy algorithm such that the sum of the values of any two vertically or horizontally adjacent cells is unique.
%C A307834 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 A307834 Rémy Sigrist, <a href="/A307834/b307834.txt">Table of n, a(n) for n = 0..10200</a> (-50 <= x <= 50 and -50 <= y <= 50)
%H A307834 Peter Kagey and Rémy Sigrist, <a href="/A307834/a307834_2.png">Colored representation of z(2*k)/abs(z(2*k))*a(2*k) for k = 1..501000</a> (where z(n) = A174344(n) + i*A274923(n) and the hue is function of k)
%H A307834 Peter Kagey and Rémy Sigrist, <a href="/A307834/a307834_3.png">Colored representation of z(2*k-1)/abs(z(2*k-1))*a(2*k-1) for k = 1..501000</a> (where z(n) = A174344(n) + i*A274923(n) and the hue is function of k)
%H A307834 Rémy Sigrist, <a href="/A307834/a307834.png">Colored illustration of the sequence (with cells (x,y) such that -500 <= x <= 500 and -500 <= y <= 500)</a>
%H A307834 Rémy Sigrist, <a href="/A307834/a307834_1.png">Colored illustration of the sequence in function of the parities of x and y</a>
%H A307834 Rémy Sigrist, <a href="/A307834/a307834.gp.txt">PARI program for A307834</a>
%e A307834 The spiral begins:
%e A307834     8--158---69--111---91---95---93--110---61--147----6
%e A307834     |                                                 |
%e A307834   164    5---96---46---67---66---62---44---86----5  140
%e A307834     |    |                                       |    |
%e A307834    67  100    4---48---32---31---31---43----4   80   64
%e A307834     |    |    |                             |    |    |
%e A307834   123   50   52    3---18---17---15----2   38   45   96
%e A307834     |    |    |    |                   |    |    |    |
%e A307834    97   71   37   20    2----2----1   13   28   51   88
%e A307834     |    |    |    |    |         |    |    |    |    |
%e A307834   102   72   39   19    5    0----0   12   26   56   82
%e A307834     |    |    |    |    |              |    |    |    |
%e A307834    99   76   34   25    1----8---10----1   35   42   94
%e A307834     |    |    |    |                        |    |    |
%e A307834   123   56   58    2---27---22---21---32----2   76   55
%e A307834     |    |    |                                  |    |
%e A307834    71  106    6---63---40---46---49---39---70----5  130
%e A307834     |    |                                            |
%e A307834   172    9--110---54---80---76---75---84---56--122----7
%e A307834     |
%e A307834    10--182---73--133--109--117--120--112--141---76--193
%o A307834 (PARI) See Links section.
%Y A307834 See A307838 for the multiplicative variant.
%Y A307834 Cf A174344, A274923.
%K A307834 nonn,look
%O A307834 0,4
%A A307834 _Rémy Sigrist_, May 01 2019