A333391 Longest side of primitive integer triangles with nonzero rational distances between three vertices and first isogonic center, sorted.

73, 95, 152, 205, 208, 280, 285, 287, 296, 343, 361, 387, 407, 437, 469, 473, 485, 497, 507, 608, 624, 633, 645, 713, 715, 728, 728, 817, 873, 931

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Leisure Maths Entertainment Forum, The primitive integer triangles with nonzero rational distances between three vertices and 1st isogonic center, Chinese blog.

Project Euler, Problem 143. Investigating the Torricelli point of a triangle

Example

Case 1: When the isogonic center is inside the triangle, i.e., the three internal angles are all less than 120 degrees: Example: Length of three sides (a, b, c) = (57, 65, 73), rational distances with signs (x, y, z) = (325/7, 264/7, 195/7);
Case 2: When the isogonic center is outside the triangle, i.e., an internal angle is greater than 120 degrees. Example: Lengths of three sides (a, b, c) = (43, 248, 285), rational distances with signs (x, y, z) = (1800/7, 345/7, -136/7);
Thus 73 and 285 are in this sequence.

Crossrefs

Cf. A070082.

Sequence in context: A325070 A152308 A072052 * A336332 A034848 A168110

Adjacent sequences: A333388 A333389 A333390 * A333392 A333393 A333394

Keyword

nonn,more

Author

Mo Li, Mar 18 2020

Status

approved