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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A330917 Largest possible side length, a, of a Heronian triangle with perimeter A051518(n), such that a <= b <= c.

Original entry on oeis.org

3, 5, 5, 6, 5, 10, 10, 8, 13, 11, 15, 16, 15, 7, 15, 20, 11, 17, 20, 20, 19, 15, 25, 26, 22, 25, 30, 29, 32, 25, 30, 25, 35, 25, 30, 39, 40, 39, 33, 34, 40, 45, 48, 38, 35, 51, 50, 53, 41, 52, 34, 43, 29, 55, 50, 35, 39, 57, 60, 65, 55, 64, 51, 65, 65, 60, 68, 61, 70, 65
Offset: 1

Views

Author

Wesley Ivan Hurt, May 03 2020

Keywords

Examples

			a(1) = 3; there is one Heronian triangle with perimeter A051518(1) = 12, which is [3,4,5] and its shortest side is 3.
a(6) = 10; there are two Heronian triangles with perimeter A051518(6) = 32, [4,13,15] and [10,10,12], whose smallest side lengths are 4 and 10. The largest of these is 10.

Links

Crossrefs

Cf. A051516, A051518, A070138, A096468, A298079, A298614, A305717.
Cf. A330912, A330915, A330916, A330921.
Cf. A330923, A331199.

A330923 Largest possible side length, b, of a Heronian triangle with perimeter A051518(n), such that a <= b <= c.

Original entry on oeis.org

4, 5, 5, 8, 12, 13, 13, 15, 15, 13, 17, 17, 25, 24, 25, 29, 25, 25, 25, 29, 20, 26, 30, 35, 26, 40, 39, 40, 41, 40, 51, 33, 48, 38, 50, 45, 58, 41, 60, 51, 65, 65, 61, 60, 56, 68, 65, 75, 50, 72, 61, 61, 60, 74, 80, 84, 68, 65, 87, 89, 90, 82, 87, 80, 89, 102, 100, 74
Offset: 1

Views

Author

Wesley Ivan Hurt, May 03 2020

Keywords

Examples

			a(1) = 4; there is one Heronian triangle with perimeter A051518(1) = 12, which is [3,4,5] and its middle side is 4.
a(6) = 13; there are two Heronian triangles with perimeter A051518(6) = 32, [4,13,15] and [10,10,12], whose middle side lengths are 13 and 10. The largest of these is 13.

Links

Crossrefs

Cf. A051516, A051518, A070138, A096468, A298079, A298614, A305717.
Cf. A330912, A330915, A330916, A330921.
Cf. A330917, A331199.

A331199 Largest possible side length, c, of a Heronian triangle with perimeter A051518(n), such that a <= b <= c.

Original entry on oeis.org

5, 6, 8, 10, 13, 15, 17, 17, 20, 20, 21, 24, 26, 25, 29, 30, 30, 26, 29, 35, 37, 37, 39, 41, 40, 41, 45, 48, 48, 51, 53, 52, 53, 51, 58, 60, 61, 50, 65, 65, 68, 70, 74, 74, 75, 75, 78, 80, 73, 82, 75, 68, 85, 87, 89, 89, 87, 87, 95, 97, 97, 97, 101, 102, 104, 106
Offset: 1

Views

Author

Wesley Ivan Hurt, May 03 2020

Keywords

Examples

			a(1) = 5; there is one Heronian triangle with perimeter A051518(1) = 12, which is [3,4,5] and its largest side length is 5.
a(6) = 15; there are two Heronian triangles with perimeter A051518(6) = 32, [4,13,15] and [10,10,12], whose largest side lengths are 15 and 12. The largest of these is 15.

Links

Crossrefs

Cf. A051516, A051518, A070138, A096468, A298079, A298614, A305717.
Cf. A330912, A330915, A330916, A330921.
Cf. A330917, A330923.

A334584 Perimeters of primitive Heronian triangles whose smallest side length is prime.

Original entry on oeis.org

12, 16, 18, 30, 42, 44, 50, 54, 56, 64, 66, 68, 70, 76, 80, 84, 90, 98, 100, 104, 108, 112, 128, 132, 140, 144, 150, 152, 156, 162, 164, 172, 174, 180, 182, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 230, 232, 234, 236, 238, 242, 248, 250, 252, 256, 260
Offset: 1

Views

Author

Wesley Ivan Hurt, May 06 2020

Keywords

Examples

			a(1) = 12; there is one primitive Heronian triangle with a perimeter of 12 whose shortest side length is prime, which is [3,4,5].
a(4) = 30; there is one primitive Heronian triangle with a perimeter of 30 whose shortest side length is prime, [5,12,13].

Links

Crossrefs

Cf. A010051, A096468, A334586, A334587.

A334586 Perimeters of primitive Heronian triangles whose middle side length is prime.

Original entry on oeis.org

16, 18, 32, 36, 44, 48, 50, 54, 64, 72, 90, 96, 98, 100, 108, 112, 128, 130, 132, 140, 144, 150, 154, 160, 162, 170, 172, 192, 196, 200, 204, 210, 224, 240, 242, 248, 250, 256, 270, 286, 290, 294, 300, 306, 318, 320, 322, 324, 336, 338, 350, 352, 356, 364, 378, 380
Offset: 1

Views

Author

Wesley Ivan Hurt, May 06 2020

Keywords

Examples

			a(1) = 16; there is one primitive Heronian triangle with a perimeter of 16 whose middle side length is prime, which is [5,5,6].
a(3) = 32; there is one primitive Heronian triangle with a perimeter of 32 whose middle side length is prime, [4,13,15].

Links

Crossrefs

Cf. A010051, A096468, A334584, A334587.

A334587 Perimeters of primitive Heronian triangles whose longest side length is prime.

Original entry on oeis.org

12, 30, 36, 40, 50, 60, 70, 76, 78, 80, 84, 90, 98, 100, 108, 112, 126, 128, 132, 144, 150, 152, 156, 160, 164, 176, 180, 182, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 230, 234, 236, 240, 242, 250, 256, 258, 260, 266, 270, 272, 286, 288, 300, 306, 320
Offset: 1

Views

Author

Wesley Ivan Hurt, May 06 2020

Keywords

Examples

			a(1) = 12; there is one primitive Heronian triangle with a perimeter of 12 whose longest side length is prime, which is [3,4,5].
a(4) = 40; there is one primitive Heronian triangle with a perimeter of 40 whose longest side length is prime, [8,15,17].

Links

Crossrefs

Cf. A010051, A096468, A334584, A334586.

A334983 Perimeters of Heronian triangles where the lengths of the smallest and largest sides are coprime.

Original entry on oeis.org

12, 16, 18, 30, 32, 36, 40, 42, 44, 48, 50, 54, 56, 60, 64, 66, 68, 70, 72, 76, 78, 80, 84, 90, 96, 98, 100, 104, 108, 110, 112, 114, 120, 126, 128, 130, 132, 140, 144, 150, 152, 154, 156, 160, 162, 164, 168, 170, 172, 174, 176, 180, 182, 186, 190, 192, 196, 198, 200, 204
Offset: 1

Views

Author

Wesley Ivan Hurt, May 18 2020

Keywords

Comments

This sequence includes the perimeters of all primitive Heronian triangles (A096468). First differs from A096468 at a(38) = 140.

Examples

			a(1) = 12; there is one Heronian triangle with perimeter 12, which is [3,4,5] and the lengths of the smallest and largest sides are coprime (GCD(3,5) = 1).
a(5) = 32; there is one Heronian triangle with perimeter 32, [4,13,15] and the lengths of the smallest and middle sides are coprime (GCD(4,13) = 1).

Links

Crossrefs

Cf. A051518, A096468, A334984, A334989.

A334984 Perimeters of Heronian triangles where the lengths of the middle and largest sides are coprime.

Original entry on oeis.org

12, 16, 18, 30, 32, 36, 40, 42, 44, 48, 50, 54, 56, 60, 64, 68, 70, 72, 76, 78, 80, 84, 90, 96, 98, 100, 104, 108, 110, 112, 114, 120, 126, 128, 130, 132, 136, 140, 144, 150, 152, 154, 156, 160, 162, 164, 168, 170, 172, 176, 180, 182, 186, 190, 192, 196, 198, 200, 204, 208
Offset: 1

Views

Author

Wesley Ivan Hurt, May 18 2020

Keywords

Comments

This sequence includes the perimeters of all primitive Heronian triangles (A096468). First differs from A096468 at a(16) = 68.

Examples

			a(1) = 12; there is one Heronian triangle with perimeter 12, which is [3,4,5] and the lengths of the middle and largest sides are coprime (GCD(4,5) = 1).
a(5) = 32; there is one Heronian triangle with perimeter 32, [4,13,15] and the lengths of the smallest and middle sides are coprime (GCD(4,13) = 1).

Links

Crossrefs

Cf. A051518, A096468, A334983, A334989.

A334989 Perimeters of Heronian triangles where the lengths of the smallest and middle sides are coprime.

Original entry on oeis.org

12, 30, 32, 36, 40, 42, 44, 48, 50, 54, 56, 60, 64, 66, 68, 70, 72, 76, 78, 80, 84, 90, 96, 98, 100, 104, 108, 110, 112, 114, 120, 126, 128, 130, 132, 136, 140, 144, 150, 152, 154, 156, 160, 162, 164, 168, 170, 172, 174, 176, 180, 182, 186, 190, 192, 196, 198, 200, 204
Offset: 1

Views

Author

Wesley Ivan Hurt, May 18 2020

Keywords

Comments

This sequence includes the perimeters of all primitive Heronian triangles (A096468). First differs from A096468 at a(2) = 30.

Examples

			a(1) = 12; there is one Heronian triangle with perimeter 12, which is [3,4,5] and the lengths of the smallest and middle sides are coprime (GCD(3,4) = 1).
a(3) = 32; there is one Heronian triangle with perimeter 32, [4,13,15] and the lengths of the smallest and middle sides are coprime (GCD(4,13) = 1).

Links

Crossrefs

Cf. A051518, A096468, A334983, A334984.

A308222 Numbers that are the perimeter of a primitive Heronian isosceles triangle.

Original entry on oeis.org

16, 18, 36, 50, 64, 98, 100, 144, 162, 196, 242, 256, 324, 338, 400, 450, 484, 576, 578, 676, 722, 784, 882, 900, 1024, 1058, 1156, 1250, 1296, 1444, 1458, 1600, 1682, 1764, 1922, 1936, 2116, 2178, 2304, 2450, 2500, 2704, 2738, 2916, 3042, 3136
Offset: 1

Views

Author

Peter Kagey, May 16 2019

Keywords

Comments

A primitive Heronian triangle is a triangle with integer sides and area, where the side lengths do not share a common divisor.

Examples

			Table illustrating first six terms of the sequence:
  perimeter |   sides    | area
  ----------+------------+-----
      16    |  (5,5,6)   |  12
      18    |  (5,5,8)   |  12
      36    | (10,13,13) |  60
      50    | (13,13,24) |  60
      50    | (16,17,17) | 120
      64    | (14,25,25) | 168
      64    | (17,17,30) | 120
      98    | (24,37,37) | 420
      98    | (25,25,48) | 168
      98    | (29,29,40) | 420

Links

Crossrefs

Cf. A046790, A096033, A096468.

Formula

a(n) = 2*A096033(n+2) (conjectured).
Previous Showing 21-30 of 35 results. Next

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