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.

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A195925 Positive integers a for which there is a (3/2)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

5, 6, 9, 10, 12, 13, 14, 15, 15, 17, 18, 18, 19, 20, 21, 21, 22, 23, 24, 25, 25, 26, 27, 27, 28, 29, 30, 30, 30, 30, 31, 32, 33, 34, 34, 35, 36, 36, 38, 38, 39, 39, 40, 42, 42, 42, 42, 43, 44, 45, 45, 45, 46, 47, 48, 48, 50, 50, 51, 51, 52, 54, 54, 54, 55, 55, 56
Offset: 1

Views

Author

Clark Kimberling, Sep 26 2011

Keywords

Comments

See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

Crossrefs

(See A195925.)

Programs

  • Mathematica
    z8 = 800; z9 = 400; z7 = 100;
k = 3/2; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]  (* A195925 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A195926 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A195927 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]  (* A195928 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A195929 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A195930 *)

A195932 Positive integers a for which there is a (-1/3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 7, 8, 8, 9, 9, 9, 9, 10, 11, 11, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 24, 25, 25, 26, 26, 27, 27, 27, 27, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 30
Offset: 1

Views

Author

Clark Kimberling, Sep 26 2011

Keywords

Comments

See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

Crossrefs

Cf. A195770, A195933, A195934, A195935.

Programs

  • Mathematica
    z8 = 800; z9 = 400; z7 = 100;
k = -1/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]   (* A195932 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]   (* A195933 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]   (* A195934 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]   (* A195935 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]   (* A195936 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]   (* A195937 *)

A195994 Positive integers a for which there is a (-2/3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

2, 4, 5, 6, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 14, 14, 14, 15, 15, 16, 16, 17, 18, 18, 18, 18, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 29, 30, 30, 30, 30, 31, 32, 32, 32, 33, 33, 34, 34, 34, 35, 35, 35
Offset: 1

Views

Author

Clark Kimberling, Sep 26 2011

Keywords

Comments

See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

Crossrefs

Cf. A195770, A195995, A195996, A195997, A195998, A195999.

Programs

  • Mathematica
    z8 = 800; z9 = 400; z7 = 100;
k = -2/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]  (* A195994 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A195995 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A195996 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]  (* A195997 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A195998 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A195999 *)

A196001 Positive integers a for which there is a (2/3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

4, 5, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 15, 16, 16, 17, 18, 18, 19, 20, 20, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 28, 29, 30, 30, 30, 31, 32, 32, 33, 33, 34, 34, 35, 35, 35, 36, 36, 36, 36, 38, 38, 39, 39, 40, 40, 40, 41, 42, 42, 42
Offset: 1

Views

Author

Clark Kimberling, Sep 26 2011

Keywords

Comments

See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

Crossrefs

Cf. A195770, A196002, A196003, A196004.

Programs

  • Mathematica
    z8 = 800; z9 = 400; z7 = 100;
k = 2/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]    (* A196001 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]    (* A196002 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]    (* A196003 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]    (* A196004 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]    (* A196005 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]    (* A196006 *)

A196008 Positive integers a for which there is a (-5/3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

3, 5, 6, 7, 8, 8, 9, 9, 10, 11, 12, 13, 14, 15, 15, 15, 16, 16, 17, 18, 18, 19, 20, 21, 21, 21, 22, 24, 24, 24, 25, 25, 26, 27, 27, 27, 27, 28, 30, 30, 30, 31, 32, 32, 32, 33, 33, 35, 35, 35, 35, 36, 36, 37, 38, 39, 39, 40, 40, 40, 40, 42, 42, 42, 43, 45, 45, 45, 45
Offset: 1

Views

Author

Clark Kimberling, Sep 27 2011

Keywords

Comments

See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

Crossrefs

Cf. A195770, A196009, A196083, A186084.

Programs

  • Mathematica
    z8 = 400; z9 = 150; z7 = 100;
k = -5/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]   (* A196008 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]   (* A196009 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]   (* A196083 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];   (* A196084 *)
x2 = Delete[f, Position[f, 0]]
g = Table[y1[n], {n, 1, z9}];   (* A196085 *)
y2 = Delete[g, Position[g, 0]]
h = Table[z1[n], {n, 1, z9}];   (* A196086 *)
z2 = Delete[h, Position[h, 0]]

A196109 Positive integers b for which there is a primitive (7/4)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

68, 38, 28, 23, 20, 18, 256, 96, 64, 564, 294, 159, 132, 32, 78, 352, 224, 790, 540, 51, 415, 290, 96, 165, 480, 791, 644, 546, 183, 350, 301, 832, 252, 128, 203, 320, 558, 154, 315, 455, 814, 693, 572, 116, 451, 330, 780, 416, 611, 896, 205, 847, 442
Offset: 1

Views

Author

Clark Kimberling, Sep 28 2011

Keywords

Comments

See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

Crossrefs

Cf. A195770, A196105, A196109, A196110.

Programs

A196119 Positive integers a for which there is a 4-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

3, 4, 5, 6, 7, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 28, 28, 28, 28, 28, 28, 29, 30, 30, 30, 31, 32
Offset: 1

Views

Author

Clark Kimberling, Sep 28 2011

Keywords

Comments

See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

Crossrefs

Cf. A195770, A196120, A196121, A196122.

Programs

  • Mathematica
    z8 = 900; z9 = 250; z7 = 200;
k = 4; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]  (* A196119 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196120 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196121 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]  (* A196122 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196123 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196124 *)

A196155 Positive integers a for which there is a 5-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

1, 2, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22
Offset: 1

Views

Author

Clark Kimberling, Sep 28 2011

Keywords

Comments

See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

Crossrefs

Cf. Ac. A195770, A196155, A196156, A196158.

Programs

  • Mathematica
    z8 = 900; z9 = 250; z7 = 200;
k = 5; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]  (* A196155 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196156 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196157 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]  (* A196158 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196159 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196160 *)

A196158 Positive integers a for which there is a primitive 5-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

1, 3, 5, 5, 5, 7, 7, 8, 8, 9, 9, 11, 11, 11, 13, 13, 13, 13, 15, 15, 16, 16, 17, 17, 17, 19, 19, 19, 21, 23, 23, 23, 24, 24, 24, 25, 25, 27, 29, 29, 31, 31, 32, 32, 33, 33, 35, 37, 39, 40, 40, 40, 40, 41, 43, 45, 47, 48, 48, 51, 53, 55, 55, 55, 56, 56, 57, 59, 61
Offset: 1

Views

Author

Clark Kimberling, Sep 28 2011

Keywords

Comments

See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

Examples

			Primitive 5-Pythagorean triples a,b,c;
c^2=a^2+b^2+k*a*b, where k=5:
1,3,5
3,40,47
5,8,17
5,32,43
5,119,131
7,69,85
7,240,257
8,11,25
8,65,83
9,40,59

Crossrefs

Cf. A195770, A196155, A196158, A196159, A196160.

Programs

A196162 Positive integers a for which there is a 6-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23
Offset: 1

Views

Author

Clark Kimberling, Sep 28 2011

Keywords

Comments

See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

Crossrefs

Cf. A195770, A196163, A196164, A196165.

Programs

  • Mathematica
    z8 = 900; z9 = 250; z7 = 200;
k = 6; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]  (* A196162 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196163 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196164 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]  (* A196165 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196166 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196167 *)
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