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A283303 List points (x,y) having integer coordinates with x >= y >= 0, sorted first by x^2+y^2 and in case of a tie, by x-coordinate. Sequence gives x-coordinates. 6

%I

%S 0,1,1,2,2,2,3,3,3,4,4,3,4,4,5,5,5,4,5,6,6,6,5,6,7,5,7,6,7,7,6,8,7,8,

%T 8,6,8,7,8,9,9,7,9,8,9,9,7,8,10,10,10,9,10,8,10,9,11,11,10,11,8,9,11,

%U 10,11,12,9,12,11,12,10,12,11,12,9,10,12,13,11,13,13,13,12,10,11,13,12,13,14

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

%H Hugo Pfoertner, <a href="/A283303/b283303.txt">Table of n, a(n) for n = 1..10000</a>

%e The first few points (listing [x^2+y^2,x,y]) are:

%e [0, 0, 0], [1, 1, 0], [2, 1, 1], [4, 2, 0], [5, 2, 1], [8, 2, 2], [9, 3, 0], [10, 3, 1], [13, 3, 2], [16, 4, 0], [17, 4, 1], [18, 3, 3], [20, 4, 2], [25, 4, 3], [25, 5, 0], [26, 5, 1], [29, 5, 2], [32, 4, 4], [34, 5, 3], [36, 6, 0], [37, 6, 1], [40, 6, 2], [41, 5, 4], [45, 6, 3], [49, 7, 0], ...

%p L:=[];

%p M:=30;

%p for i from 0 to M do

%p for j from 0 to i do

%p L:=[op(L),[i^2+j^2,i,j]]; od: od:

%p t3:= sort(L,proc(a,b) evalb(a[1]<=b[1]); end);

%p t3x:=[seq(t3[i][2],i=1..100)]; # A283303

%p t3y:=[seq(t3[i][3],i=1..100)]; # A283304

%Y For the y coordinates see A283304.

%Y See also A283305-A283308.

%K nonn

%O 1,4

%A _N. J. A. Sloane_, Mar 04 2017, following a suggestion from _Ahmet Arduç_.

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Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)