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A283306
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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 y-coordinates.
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5
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0, 1, 0, 1, 2, 0, 2, 1, 2, 3, 0, 3, 1, 3, 2, 4, 0, 4, 1, 3, 4, 2, 5, 4, 3, 0, 5, 1, 5, 2, 4, 5, 3, 6, 0, 6, 1, 6, 2, 5, 4, 6, 3, 7, 0, 7, 5, 1, 6, 4, 7, 2, 7, 3, 6, 5, 8, 0, 8, 7, 4, 1, 8, 2, 6, 8, 3, 7, 5, 8, 4, 9, 0, 9, 1, 9, 7, 6, 2, 8, 5, 9, 3, 9, 4, 7, 10, 8, 6, 0, 10, 1, 10, 2, 9, 5, 10, 3, 8, 7
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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LINKS
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EXAMPLE
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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], ...
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MAPLE
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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
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MATHEMATICA
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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, 2]]& // PadRight[#, nt]&
S[m = 2];
S[m = 2m];
While[S[m] =!= S[m/2], m = 2m];
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PROG
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(PARI) for(r2=0, 113, for(x=0, round(sqrt(r2)), y2=r2-x^2; if(issquare(y2), print1(round(sqrt(y2)), ", ")))) \\ Hugo Pfoertner, Jun 18 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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