
COMMENTS

A closetoequilateral integer triangle is defined to be a triangle with integer sides and integer area such that the largest and smallest sides differ in length by unity. The first five closetoequilateral integer triangles have sides (5, 5, 6), (17, 17, 16), (65, 65, 66), (241, 241, 240) and (901, 901, 902).
Next four terms are: {three sides a<b<c and area} { 46816, 46817, 46817, 949077360}, { 174725, 174725, 174726, 13219419708}, { 652080, 652081, 652081, 184120982760}, {2433601, 2433601, 2433602, 2564481115560}. Also, the first case {1,1,2,0}  integer triangle with zero area, fully appropriate to definition of 'closetoequilateral' one, should be added. We have 12 cases and a weak conjecture is that the total number of the 'closetoequilateral' triangles is finite.  Zak Seidov, Feb 23 2005
This is an infinite series; two sides are equal in length to the hypotenuse of almost 3060 triangles and the third side alternates between that length +/ 1.  Dan Sanders (dan(AT)ified.ca), Oct 22 2005
