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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A196362 Positive integers a for which there is a (-5/2)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 01 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A196363, A196364, A196365.

Programs

  • Mathematica
    z8 = 900; z9 = 250; z7 = 200;
pIntegerQ := IntegerQ[#1] && #1 > 0 &;
k = -5/2; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[pIntegerQ[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}]  (* A196362 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196363 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196364 *)
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]]  (* A196365 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196366 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196367 *)

A196369 Positive integers a for which there is a (-3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 01 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A196370, A196371, A196372.

Programs

  • Mathematica
    z8 = 900; z9 = 250; z7 = 200;
pIntegerQ := IntegerQ[#1] && #1 > 0 &;
k = -3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[pIntegerQ[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}]  (* A196369 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196370 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196371 *)
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]]  (* A196372 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196373 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196374 *)

A196376 Positive integers a for which there is a (-4)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 01 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A196377, A196378, A196379.

Programs

  • Mathematica
    z8 = 900; z9 = 250; z7 = 200;
pIntegerQ := IntegerQ[#1] && #1 > 0 &;
k = -4; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[pIntegerQ[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}]  (* A196376 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196377 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196378 *)
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]]  (* A196379 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196380 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196381 *)

A196390 Positive integers a for which there is a (-6)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 01 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A196391, A196392, A196393.

Programs

  • Mathematica
    z8 = 900; z9 = 250; z7 = 200;
pIntegerQ := IntegerQ[#1] && #1 > 0 &;
k = -6; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[pIntegerQ[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}]  (* A196390 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196391 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196392 *)
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]]  (* A196393 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196394 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196395 *)

A196028 Positive integers c for which there is a (5/2)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

28, 20, 18, 91, 56, 45, 40, 190, 36, 110, 84, 35, 325, 60, 182, 135, 112, 54, 496, 90, 272, 198, 80, 77, 140, 703, 126, 380, 273, 72, 220, 104, 100, 168, 506, 360, 70, 143, 135, 216, 650, 90, 196, 459, 120, 364, 170, 88, 270, 812, 570, 224, 209, 108, 140
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, A196026.

Programs

A196029 Positive integers a for which there is a primitive (5/2)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

5, 6, 7, 9, 11, 13, 14, 16, 17, 19, 21, 22, 23, 25, 25, 26, 29, 30, 31, 32, 34, 35, 37, 38, 38, 41, 43, 46, 47, 48, 49, 50, 53, 58, 61, 62, 64, 64, 65, 65, 70, 73, 77, 80, 80, 85, 85, 86, 94, 105, 105, 110, 110, 112, 112, 118, 128
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.

Examples

			Primitive (5/2)-Pythagorean triples
(c^2=a^2+b^2+k*a*b, where k=5/2):
5,22,28
6,13,20
7,10,18
9,80,91
11,32,45
13,174,190
14,93,110
16,17,35
17,304,325
19,112,135

Crossrefs

Cf. A195770, A196026, A196030, A196031.

Programs

A196040 Positive integers a for which there is a (4/3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

7, 8, 9, 11, 13, 14, 15, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 26, 27, 27, 28, 28, 29, 30, 32, 33, 33, 34, 35, 36, 36, 39, 39, 40, 40, 40, 41, 42, 44, 44, 45, 45, 46, 47, 48, 48, 49, 51, 52, 54, 54, 55, 56, 56, 56, 57, 58, 60, 60, 63, 63, 63, 63, 64, 64, 66, 68
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, A196041, A196042, A196043.

Programs

  • Mathematica
    z8 = 800; z9 = 200; z7 = 200;
k = -4/3; 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}]   (* A196033 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]   (* A196034 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]   (* A196035 *)
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]]   (* A196036 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]   (* A196037 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]   (* A196038 *)

A196085 Positive integers b for which there is a primitive (-5/3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

5, 27, 9, 9, 21, 32, 120, 24, 16, 279, 45, 152, 504, 72, 40, 245, 795, 105, 261, 48, 72, 144, 497, 63, 189, 56, 91, 104, 656, 215, 240, 112, 225, 765, 360, 65, 160, 185, 135, 207, 429, 187, 85, 95, 155, 455, 504, 171, 585, 117, 153, 247, 672, 280, 765
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, A196008, A196084, A196085.

Programs

A196092 Positive integers b for which there is a primitive (5/3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

39, 17, 144, 56, 45, 315, 24, 552, 200, 45, 305, 72, 57, 333, 105, 581, 144, 752, 189, 63, 240, 80, 297, 360, 335, 91, 112, 504, 192, 369, 585, 160, 672, 623, 248, 765, 135, 247, 387, 280, 365, 231, 352, 216, 391, 648, 475, 351, 520, 665, 395, 667, 423
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. A175770, A196088, A196091, A196093.

Programs

A196093 Positive integers c for which there is a primitive (5/3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

45, 25, 155, 69, 59, 331, 45, 573, 223, 71, 333, 103, 93, 367, 141, 619, 185, 795, 235, 113, 291, 137, 353, 421, 397, 159, 185, 575, 267, 445, 661, 243, 753, 705, 335, 851, 229, 345, 487, 383, 467, 345, 465, 335, 509, 773, 603, 485, 653, 797, 543, 815
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, A196088, A196091, A196092.

Programs

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