1,1

A close-to-equilateral 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 close-to-equilateral 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 'close-to-equilateral' one, should be added. We have 12 cases and a weak conjecture is that the total number of the 'close-to-equilateral' triangles is finite. - Zak Seidov (zakseidov(AT)yahoo.com), Feb 23 2005

This is an infinite series; two sides are equal in length to the hypotenuse of almost 30-60 triangles and the third side alternates between that length +/- 1. - Dan Sanders (dan(AT)ified.ca), Oct 22 2005

Eric Weisstein's World of Mathematics, Heronian Triangle.

Steven Dutch, Almost 30-60 Triples

(2/3) [A007655(n+2) - (-1)^n*A001353(n+1) ] (conjectured). - Ralf Stephan, May 17 2007

a(2) = 120 because 120 is the area of a triangle with side lengths of 16, 17 and 17.

Sequence in context: A120585 A012565 A012621 this_sequence A009078 A009149 A010570

Adjacent sequences: A102338 A102339 A102340 this_sequence A102342 A102343 A102344

easy,nonn

Johannes Koelman (Joc_Kay(AT)hotmail.com), Feb 20 2005

More terms from Zak Seidov (zakseidov(AT)yahoo.com), Feb 23 2005

More terms from Dan Sanders (dan(AT)ified.ca), Oct 22 2005