A333917 Perimeters of integer-sided triangles whose altitude from their longest side is an integer.
16, 18, 32, 36, 48, 50, 54, 60, 64, 70, 72, 80, 90, 96, 98, 100, 108, 112, 120, 126, 128, 132, 140, 144, 150, 154, 160, 162, 168, 176, 180, 192, 196, 198, 200, 208, 210, 216, 220, 224, 234, 240, 242, 250, 252, 256, 260, 264, 270, 272, 280, 286, 288, 290, 294, 300
Offset: 1
Keywords
Examples
16 is in the sequence since it is the perimeter of the triangle [5,5,6], whose altitude from 6 (the longest side) is 4 (an integer). 18 is in the sequence since it is the perimeter of the triangle [5,5,8], whose altitude from 8 (the longest side) is 3 (an integer). 48 is in the sequence since it is the perimeter of the triangles [15,15,18] and [10,17,21], whose altitudes from their longest sides are 12 and 8 respectively (both integers).
Links
- Eric Weisstein's World of Mathematics, Altitude
- Wikipedia, Altitude (triangle)
- Wikipedia, Integer Triangle
Programs
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Mathematica
Flatten[Table[If[Sum[Sum[(1 - Ceiling[2*Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/(n - i - k)] + Floor[2*Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/(n - i - k)]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 100}]]