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A283307 List points (x,y) having integer coordinates, sorted first by x^2+y^2 and in case of ties, by x-coordinate and then by y-coordinate. Sequence gives x-coordinates.

%I A283307 #19 Jul 09 2025 04:43:07
%S A283307 0,-1,0,0,1,-1,-1,1,1,-2,0,0,2,-2,-2,-1,-1,1,1,2,2,-2,-2,2,2,-3,0,0,3,
%T A283307 -3,-3,-1,-1,1,1,3,3,-3,-3,-2,-2,2,2,3,3,-4,0,0,4,-4,-4,-1,-1,1,1,4,4,
%U A283307 -3,-3,3,3,-4,-4,-2,-2,2,2,4,4,-5,-4,-4,-3,-3,0,0,3,3,4,4,5,-5,-5,-1,-1,1
%N A283307 List points (x,y) having integer coordinates, sorted first by x^2+y^2 and in case of ties, by x-coordinate and then by y-coordinate. Sequence gives x-coordinates.
%e A283307 The first few points (listing [x^2+y^2,x,y]) are: [0, 0, 0], [1, -1, 0], [1, 0, -1], [1, 0, 1], [1, 1, 0], [2, -1, -1], [2, -1, 1], [2, 1, -1], [2, 1, 1], [4, -2, 0], [4, 0, -2], [4, 0, 2], [4, 2, 0], [5, -2, -1], [5, -2, 1], [5, -1, -2], [5, -1, 2], [5, 1, -2], [5, 1, 2], [5, 2, -1], [5, 2, 1], [8, -2, -2], [8, -2, 2], [8, 2, -2], ...
%p A283307 L:=[];
%p A283307 M:=30;
%p A283307 for i from -M to M do
%p A283307 for j from -M to M do
%p A283307 L:=[op(L),[i^2+j^2,i,j]]; od: od:
%p A283307 t6:= sort(L,proc(a,b) evalb(a[1]<=b[1]); end);
%p A283307 t6x:=[seq(t6[i][2],i=1..100)]; # A283307
%p A283307 t6y:=[seq(t6[i][3],i=1..100)]; # A283308
%o A283307 (PARI) pt(t)=print1(t,", ");for(r2=0,26,xm=round(sqrt(r2));for(x=-xm,xm,y2=r2-x^2;if(issquare(y2),if(y2!=0,pt(x));pt(x)))) \\ _Hugo Pfoertner_, Jun 18 2018
%Y A283307 For the y coordinates see A283308.
%Y A283307 Cf. A004018, A283303, A283304, A283305, A283306, A305575, A305576.
%K A283307 sign
%O A283307 1,10
%A A283307 _N. J. A. Sloane_, Mar 04 2017, following a suggestion from _Ahmet Arduç_