A283308 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 y-coordinates.

0, 0, -1, 1, 0, -1, 1, -1, 1, 0, -2, 2, 0, -1, 1, -2, 2, -2, 2, -1, 1, -2, 2, -2, 2, 0, -3, 3, 0, -1, 1, -3, 3, -3, 3, -1, 1, -2, 2, -3, 3, -3, 3, -2, 2, 0, -4, 4, 0, -1, 1, -4, 4, -4, 4, -1, 1, -3, 3, -3, 3, -2, 2, -4, 4, -4, 4, -2, 2, 0, -3, 3, -4, 4, -5, 5, -4, 4, -3, 3, 0, -1, 1, -5, 5, -5, 5

Offset

1,11

Links

Table of n, a(n) for n=1..87.

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) rs(t)=round(sqrt(abs(t))); pt(t)=print1(rs(t)*sign(t), ", "); for(r2=0, 26, xm=rs(r2); for(x=-xm, xm, y2=r2-x^2; if(issquare(y2), if(y2==0, pt(0), pt(-y2); pt(y2))))) \\ Hugo Pfoertner, Jun 18 2018

Crossrefs

For the x coordinates see A283307.

Cf. A004018, A228108, A283303, A283304, A283305, A283306, A305575, A305576.

Sequence in context: A287451 A113414 A286653 * A339959 A255636 A292085

Adjacent sequences: A283305 A283306 A283307 * A283309 A283310 A283311

Keyword

sign

Author

N. J. A. Sloane, Mar 04 2017, following a suggestion from Ahmet Arduç

Status

approved