cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Ahmet Arduç

Ahmet Arduç's wiki page.

Ahmet Arduç has authored 6 sequences.

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.

Original entry on oeis.org

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

Views

Author

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

Keywords

Examples

			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], ...

Crossrefs

For the x coordinates see A283307.
Cf. A004018, A228108, A283303, A283304, A283305, A283306, A305575, A305576.

Programs

  • 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
  • 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

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.

Original entry on oeis.org

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

Views

Author

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

Keywords

Examples

			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], ...

Crossrefs

For the y coordinates see A283308.
Cf. A004018, A283303, A283304, A283305, A283306, A305575, A305576.

Programs

  • 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
  • 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

A283306 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.

Original entry on oeis.org

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
Offset: 1

Views

Author

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

Keywords

Examples

			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], ...

Crossrefs

For the x coordinates see A283305.
See also A283303, A283304.

Programs

  • 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, 2]]& // PadRight[#, nt]&
S[m = 2];
S[m = 2m];
While[S[m] =!= S[m/2], m = 2m];
S[m] (* Jean-François Alcover, Mar 05 2023 *)
  • 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

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.

Original entry on oeis.org

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

Views

Author

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

Keywords

Examples

			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], ...

Crossrefs

For the y coordinates see A283306.
See also A000925, A283303, A283304, A283307, A283308.

Programs

  • 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 *)
  • 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

A283304 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 y-coordinates.

Original entry on oeis.org

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

Views

Author

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

Keywords

Examples

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

Links

Crossrefs

For the x coordinates see A283303.
See also A283305-A283308.

Programs

  • Maple
    L:=[];
M:=30;
for i from 0 to M do
for j from 0 to i do
L:=[op(L),[i^2+j^2,i,j]]; od: od:
t3:= sort(L,proc(a,b) evalb(a[1]<=b[1]); end);
t3x:=[seq(t3[i][2],i=1..100)]; # A283303
t3y:=[seq(t3[i][3],i=1..100)]; # A283304
  • Mathematica
    nt = 105; (* number of terms to produce *)
S[m_] := S[m] = Table[{x, y}, {y, 0, m}, {x, y, m}] // Flatten[#, 1]& // SortBy[#, {#.#&, #[[1]]&}]& // #[[All, 2]]& // PadRight[#, nt]&
S[m = 2];
S[m = 2 m];
While[S[m] =!= S[m/2], m = 2 m];
S[m] (* Jean-François Alcover, Mar 05 2023 *)

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.

Original entry on oeis.org

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, 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, 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
Offset: 1

Views

Author

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

Keywords

Examples

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

Links

Crossrefs

For the y coordinates see A283304.
See also A283305-A283308.

Programs

  • Maple
    L:=[];
M:=30;
for i from 0 to M do
for j from 0 to i do
L:=[op(L),[i^2+j^2,i,j]]; od: od:
t3:= sort(L,proc(a,b) evalb(a[1]<=b[1]); end);
t3x:=[seq(t3[i][2],i=1..100)]; # A283303
t3y:=[seq(t3[i][3],i=1..100)]; # A283304
  • Mathematica
    nt = 105; (* number of terms to produce *)
S[m_] := S[m] = Table[{x, y}, {y, 0, m}, {x, y, m}] // Flatten[#, 1]& // SortBy[#, {#.#&, #[[1]]&}]& // #[[All, 1]]& // PadRight[#, nt]&
S[m = 2];
S[m = 2 m];
While[S[m] =!= S[m/2], m = 2 m];
S[m] (* Jean-François Alcover, Mar 05 2023 *)

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