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 1-3 of 3 results.

A333918 Perimeters of integer-sided triangles whose altitude from their shortest side is an integer.

Original entry on oeis.org

12, 24, 30, 32, 36, 40, 42, 44, 48, 50, 54, 56, 60, 64, 66, 68, 70, 72, 76, 80, 84, 88, 90, 96, 98, 100, 104, 108, 112, 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
Offset: 1

Views

Author

Wesley Ivan Hurt, Apr 09 2020

Keywords

Links

Crossrefs

Cf. A005044, A333917, A333919.

Programs

  • Mathematica
    Flatten[Table[If[Sum[Sum[(1 - Ceiling[2*Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/k] + Floor[2*Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/k]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 100}]]

Formula

12 is in the sequence since it is the perimeter of the triangle [3,4,5], whose altitude from 3 (the shortest side) is 4 (an integer).
24 is in the sequence since it is the perimeter of the triangle [6,8,10], whose altitude from 6 (the shortest side) is 8 (an integer).
54 is in the sequence since it is the perimeter of the triangles [3,25,26] and [12,17,25] whose altitudes from their shortest sides are 24 and 15 respectively (both integers).

A333919 Perimeters of integer-sided triangles with side lengths a <= b <= c whose altitude from side b is an integer.

Original entry on oeis.org

12, 24, 30, 36, 40, 42, 48, 56, 60, 70, 72, 78, 80, 84, 90, 96, 104, 108, 110, 112, 114, 120, 126, 132, 136, 140, 144, 150, 154, 156, 160, 162, 168, 176, 180, 182, 186, 192, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 230, 232, 234, 238, 240, 250, 252
Offset: 1

Views

Author

Wesley Ivan Hurt, Apr 09 2020

Keywords

Examples

			12 is in the sequence since it is the perimeter of the triangle [3,4,5], whose altitude from 4 (its "middle" side) is 3 (an integer).
24 is in the sequence since it is the perimeter of the triangle [6,8,10], whose altitude from 8 (its "middle" side) is 6 (an integer).
60 is in the sequence since it is the perimeter of the triangles [10,24,26] and [15,20,25], whose altitudes (from their "middle" sides) are 10 and 15 respectively (both integers).

Links

Crossrefs

Cf. A005044, A333917, A333918.

Programs

  • Mathematica
    Flatten[Table[If[Sum[Sum[(1 - Ceiling[2*Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/i] + Floor[2*Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/i]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 100}]]

A333869 Perimeters of integer-sided triangles with at least one prime altitude.

Original entry on oeis.org

12, 18, 30, 50, 56, 98, 132, 182, 242, 306, 338, 380, 552, 578, 722, 870, 992, 1058, 1406, 1682, 1722, 1892, 1922, 2256, 2738, 2862, 3362, 3540, 3698, 3782, 4418, 4556, 5112, 5402, 5618, 6320, 6962, 6972, 7442, 8010, 8978, 9506, 10082, 10302, 10658, 10712, 11556
Offset: 1

Views

Author

Wesley Ivan Hurt, Apr 10 2020

Keywords

Examples

			12 is in the sequence since it is the perimeter of the triangle [3,4,5], whose altitude from 4 (its "middle" side) is 3 (prime).
18 is in the sequence since it is the perimeter of the triangle [5,5,8], whose altitude from 8 (its longest side) is 3 (prime).

Links

Crossrefs

Cf. A005044, A333917, A333918, A333919.

Extensions

a(10)-a(29) from Jinyuan Wang, Apr 11 2020
Terms a(30) and beyond from Giovanni Resta, Apr 12 2020
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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