Discussion of A268602 by the Editors, Apr 22 2023
Jinyuan Wang: The name is not correct: (1519/492, 4920/1519, 3344161/747) has a smaller hypotenuse with area 5 than (3/2, 20/3, 41/6). But there are different understandings of "the easiest Pythagorean Triangle":
03:59	
Jinyuan Wang: I referred to the tables in https://arxiv.org/pdf/2106.07373.pdf, http://bitman.name/math/table/29 and http://www.kaynet.or.jp/~kay/misc/congr.html. The first link define the “height” of the representation as max(α1, α2, β1, β2) where α = α1/α2, β = β1/β2 are the rational sides as the quotients of relatively prime integers. So the easiest Pythagorean Triangle has the smallest height. The table in the second link has a typo: for n=31, r should be 103320. It believes the easiest Pythagorean Triangle has the smallest numerator of hypotenuse. But the sequences derived from these two definitions differ from n=219 (see page 2 in the first link).
Michel Marcus: like in history ?
Jinyuan Wang: Yes the same terms in history, but which definiton of "the easiest Pythagorean Triangle" should we adopt? Although this won't affect the first few terms