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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.
5
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, -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, -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
OFFSET
1,10
EXAMPLE
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], ...
MAPLE
L:=[];
M:=30;
for i from -M to M do
for j from -M to M do
L:=[op(L), [i^2+j^2, i, j]]; od: od:
t6:= sort(L, proc(a, b) evalb(a[1]<=b[1]); end);
t6x:=[seq(t6[i][2], i=1..100)]; # A283307
t6y:=[seq(t6[i][3], i=1..100)]; # A283308
PROG
(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
CROSSREFS
For the y coordinates see A283308.
Sequence in context: A277328 A318178 A363485 * A273514 A048866 A262904
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Mar 04 2017, following a suggestion from Ahmet Arduç.
STATUS
approved