A283305 List points (x,y) having integer coordinates with x >= 0, y >= 0, sorted first by x^2+y^2 and in case of a tie, by x-coordinate. Sequence gives x-coordinates.

0, 0, 1, 1, 0, 2, 1, 2, 2, 0, 3, 1, 3, 2, 3, 0, 4, 1, 4, 3, 2, 4, 0, 3, 4, 5, 1, 5, 2, 5, 4, 3, 5, 0, 6, 1, 6, 2, 6, 4, 5, 3, 6, 0, 7, 1, 5, 7, 4, 6, 2, 7, 3, 7, 5, 6, 0, 8, 1, 4, 7, 8, 2, 8, 6, 3, 8, 5, 7, 4, 8, 0, 9, 1, 9, 2, 6, 7, 9, 5, 8, 3, 9, 4, 9, 7, 0, 6, 8, 10, 1, 10, 2, 10, 5, 9, 3, 10, 7, 8

Offset

1,6

Links

Table of n, a(n) for n=1..100.

Example

The first few points (listing [x^2+y^2,x,y]) are: [0, 0, 0], [1, 0, 1], [1, 1, 0], [2, 1, 1], [4, 0, 2], [4, 2, 0], [5, 1, 2], [5, 2, 1], [8, 2, 2], [9, 0, 3], [9, 3, 0], [10, 1, 3], [10, 3, 1], [13, 2, 3], [13, 3, 2], [16, 0, 4], [16, 4, 0], [17, 1, 4], [17, 4, 1], [18, 3, 3], [20, 2, 4], [20, 4, 2], [25, 0, 5], [25, 3, 4], [25, 4, 3], ...

Maple

L:=[];
M:=30;
for i from 0 to M do
for j from 0 to M do
L:=[op(L), [i^2+j^2, i, j]]; od: od:
t4:= sort(L, proc(a, b) evalb(a[1]<=b[1]); end);
t4x:=[seq(t4[i][2], i=1..100)]; # A283305
t4y:=[seq(t4[i][3], i=1..100)]; # A283306

Mathematica

nt = 105; (* number of terms to produce *)
S[m_] := S[m] = Table[{x, y}, {x, 0, m}, {y, 0, m}] // Flatten[#, 1]& // SortBy[#, {#.#&, #[[1]]&}]& // #[[All, 1]]& // PadRight[#, nt]&;
S[m = 2];
S[m = 2m];
While[S[m] =!= S[m/2], m = 2m];
S[m] (* Jean-François Alcover, Mar 05 2023 *)

Prog

(PARI) for(r2=0, 113, for(x=0, round(sqrt(r2)), y2=r2-x^2; if(issquare(y2), print1(x, ", ")))) \\ Hugo Pfoertner, Jun 18 2018

Crossrefs

For the y coordinates see A283306.

See also A000925, A283303, A283304, A283307, A283308.

Sequence in context: A137579 A337108 A108805 * A226005 A134343 A008441

Adjacent sequences: A283302 A283303 A283304 * A283306 A283307 A283308

Keyword

nonn

Author

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

Status

approved