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.

Showing 1-10 of 35 results. Next

A298614 Number of primitive Heronian triangles with perimeter A096468(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 3, 1, 1, 2, 1, 1, 1, 2, 5, 3, 1, 6, 3, 2, 5, 1, 4, 1, 1, 1, 4, 1, 6, 1, 3, 4, 5, 1, 3, 3, 2, 8, 1, 1, 1, 1, 1, 5, 1, 3, 2, 2, 7, 8, 3, 4, 3, 2, 6, 3, 3, 1, 5, 4, 3, 1, 5, 1, 2, 6, 16, 1, 9, 4, 9, 1, 3, 2, 3, 1, 4
Offset: 1

Views

Author

Peter Kagey, Jan 26 2018

Keywords

Comments

A Heronian triangle is a triangle with integer sides and area.

Crossrefs

This is A070138 with the zeros omitted.
Cf. A096468.

Formula

a(n) = A070138(A096468(n)).

A330874 Sum of the smallest side lengths of all primitive Heronian triangles with perimeter A096468(n).

Original entry on oeis.org

3, 5, 5, 5, 4, 19, 8, 20, 11, 10, 29, 28, 7, 6, 36, 11, 17, 37, 8, 19, 15, 29, 69, 47, 15, 133, 64, 38, 71, 25, 100, 25, 25, 28, 97, 39, 132, 20, 46, 84, 142, 19, 103, 93, 67, 242, 41, 40, 34, 43, 29, 179, 41, 76, 70, 95, 267, 301, 69, 192, 119, 68, 178, 136, 99, 61, 201, 218
Offset: 1

Views

Author

Wesley Ivan Hurt, May 16 2020

Keywords

Examples

			a(1) = 3; there is one primitive Heronian triangle with perimeter A096468(1) = 12, [3,4,5] and 3 is the smallest side length.
a(6) = 19; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13]. The sum of the smallest side lengths is then 9 + 10 = 19.
		

Crossrefs

A331210 Largest possible side length, a, of a primitive Heronian triangle with perimeter A096468(n), such that a <= b <= c.

Original entry on oeis.org

3, 5, 5, 5, 4, 10, 8, 13, 11, 10, 16, 13, 7, 6, 17, 11, 17, 20, 8, 19, 15, 16, 17, 25, 15, 29, 29, 25, 27, 25, 29, 25, 25, 28, 37, 39, 33, 20, 25, 37, 41, 19, 35, 51, 35, 53, 41, 40, 34, 43, 29, 48, 41, 35, 39, 57, 56, 65, 36, 52, 51, 39, 41, 53, 68, 61, 60, 65, 61, 41
Offset: 1

Views

Author

Wesley Ivan Hurt, May 03 2020

Keywords

Examples

			a(1) = 3; there is one primitive Heronian triangle with perimeter A096468(1) = 12, which is [3,4,5] and its shortest side length is 3.
a(6) = 10; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13] with shortest side lengths 9 and 10. The largest of these is 10.
		

Crossrefs

A331263 Largest possible side length, b, of a primitive Heronian triangle with perimeter A096468(n), such that a <= b <= c.

Original entry on oeis.org

4, 5, 5, 12, 13, 13, 15, 15, 13, 17, 17, 25, 24, 25, 29, 25, 25, 25, 29, 20, 26, 30, 35, 40, 37, 40, 41, 40, 51, 33, 41, 38, 39, 45, 53, 41, 60, 51, 65, 65, 61, 60, 56, 68, 53, 73, 50, 51, 61, 61, 60, 74, 50, 84, 68, 65, 82, 89, 90, 73, 87, 80, 89, 85, 100, 74, 91, 82
Offset: 1

Views

Author

Wesley Ivan Hurt, May 03 2020

Keywords

Crossrefs

Formula

a(1) = 4; there is one primitive Heronian triangle with perimeter A096468(1) = 12, which is [3,4,5] and its middle side length is 4.
a(6) = 13; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13] with middle side lengths 10 and 13. The largest of these is 13.

A331264 Largest possible side length, c, of a primitive Heronian triangle with perimeter A096468(n), such that a <= b <= c.

Original entry on oeis.org

5, 6, 8, 13, 15, 17, 17, 20, 20, 21, 24, 26, 25, 29, 30, 30, 26, 29, 35, 37, 37, 39, 41, 41, 44, 48, 44, 51, 53, 52, 53, 51, 56, 53, 61, 50, 65, 65, 68, 70, 74, 73, 75, 75, 75, 80, 73, 77, 75, 68, 85, 87, 89, 89, 87, 87, 95, 97, 97, 97, 101, 101, 104, 97, 109, 87, 111
Offset: 1

Views

Author

Wesley Ivan Hurt, May 03 2020

Keywords

Examples

			a(1) = 5; there is one primitive Heronian triangle with perimeter A096468(1) = 12, which is [3,4,5] and its longest side length is 5.
a(6) = 17; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13] with longest side lengths 17 and 13. The largest of these is 17.
		

Crossrefs

A334018 Sum of the middle side lengths of all primitive Heronian triangles with perimeter A096468(n).

Original entry on oeis.org

4, 5, 5, 12, 13, 23, 15, 29, 13, 17, 30, 62, 24, 25, 71, 25, 25, 46, 29, 20, 26, 55, 160, 106, 37, 205, 109, 79, 209, 33, 146, 38, 39, 45, 195, 41, 296, 51, 178, 226, 266, 60, 153, 172, 105, 486, 50, 51, 61, 61, 60, 297, 50, 214, 130, 130, 476, 565, 252, 258, 192, 158, 493
Offset: 1

Views

Author

Wesley Ivan Hurt, May 16 2020

Keywords

Examples

			a(1) = 4; there is one primitive Heronian triangle with perimeter A096468(1) = 12, [3,4,5] and 4 is the middle side length.
a(6) = 23; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13]. The sum of the middle side lengths is then 10 + 13 = 23.
		

Crossrefs

A334120 Sum of the largest side lengths of all primitive Heronian triangles with perimeter A096468(n).

Original entry on oeis.org

5, 6, 8, 13, 15, 30, 17, 35, 20, 21, 41, 72, 25, 29, 85, 30, 26, 57, 35, 37, 37, 76, 191, 117, 44, 250, 127, 91, 260, 52, 202, 51, 56, 53, 220, 50, 364, 65, 196, 266, 342, 73, 206, 203, 148, 568, 73, 77, 75, 68, 85, 404, 89, 256, 172, 155, 601, 702, 273, 350, 301, 190, 589
Offset: 1

Views

Author

Wesley Ivan Hurt, May 16 2020

Keywords

Examples

			a(1) = 5; there is one primitive Heronian triangle with perimeter A096468(1) = 12, [3,4,5] and 5 is the largest side length.
a(6) = 30; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13]. The sum of the largest side lengths is then 17 + 13 = 30.
		

Crossrefs

A334920 Sum of the even side lengths of all primitive Heronian triangles with perimeter A096468(n).

Original entry on oeis.org

4, 6, 8, 12, 4, 20, 8, 34, 20, 10, 40, 58, 24, 6, 74, 30, 26, 48, 8, 20, 26, 46, 112, 116, 44, 226, 104, 80, 180, 52, 148, 38, 56, 28, 176, 50, 250, 20, 134, 178, 278, 60, 166, 172, 84, 506, 50, 40, 34, 68, 60, 296, 50, 194, 130, 106, 372, 494, 148, 228, 252, 158, 552, 224
Offset: 1

Views

Author

Wesley Ivan Hurt, May 16 2020

Keywords

Examples

			a(1) = 4; there is one primitive Heronian triangle with perimeter A096468(1) = 12, which is [3,4,5] and its even side length is 4.
a(6) = 20; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13]. The sum of the even side lengths is 10 + 10 = 20.
		

Crossrefs

A334927 Largest possible even side length of a primitive Heronian triangle with perimeter A096468(n).

Original entry on oeis.org

4, 6, 8, 12, 4, 10, 8, 20, 20, 10, 24, 26, 24, 6, 30, 30, 26, 28, 8, 20, 26, 30, 34, 40, 44, 48, 44, 40, 52, 52, 50, 38, 56, 28, 52, 50, 60, 20, 68, 70, 74, 60, 66, 68, 52, 80, 50, 40, 34, 68, 60, 82, 50, 84, 68, 68, 82, 92, 90, 72, 100, 80, 104, 92, 100, 74, 96, 106, 100, 104
Offset: 1

Views

Author

Wesley Ivan Hurt, May 16 2020

Keywords

Examples

			a(1) = 4; there is one primitive Heronian triangle with perimeter A096468(1) = 12, which is [3,4,5] and its largest even side length is 4.
a(6) = 10; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13]. The largest even side length of the two triangles is 10.
		

Crossrefs

A334928 Sum of the odd side lengths of all primitive Heronian triangles with perimeter A096468(n).

Original entry on oeis.org

8, 10, 10, 18, 28, 52, 32, 50, 24, 38, 60, 104, 32, 54, 118, 36, 42, 92, 64, 56, 52, 114, 308, 154, 52, 362, 196, 128, 360, 58, 300, 76, 64, 98, 336, 80, 542, 116, 286, 398, 472, 92, 296, 296, 236, 790, 114, 128, 136, 104, 114, 584, 130, 352, 242, 274, 972, 1074, 446, 572, 360
Offset: 1

Views

Author

Wesley Ivan Hurt, May 16 2020

Keywords

Examples

			a(1) = 8; there is one primitive Heronian triangle with perimeter A096468(1) = 12, which is [3,4,5] and the sum of its odd side lengths is 3 + 5 = 8.
a(6) = 52; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13]. The sum of the odd side lengths is 9 + 17 + 13 + 13 = 52.
		

Crossrefs

Showing 1-10 of 35 results. Next