Pythagorean Primitives

I hope this question is clear. If not, please suggest a change to make the
intention clearer (assuming you can work the intention out)...

Most of us are familiar with the (3, 4, 5) right-triangle. 5 is the
smallest integer hypotenuse which supports two other sides of a right-
triangle with integer length. There are many other right-triangles with
integer sides, such as: (5, 12, 13) and (8, 15, 17). These triples are
considered primitive as the terms do not share a common factor.

On the other hand, although (6, 8, 10) is a right-triangle, it is NOT
primitive as the elements share a common factor, 2.

Can you find the first four terms in the series where a(n) is the least
hypotenuse of which 2^(n-1) Pythagorean triples are primitive? So, 5 is
the smallest and supports one triple. Can you find a hypotenuse that
supports two discrete primitive Pythagorean triples, four and eight?

Good luck.
--
David Entwistle