<begin> For a triangle with integer sides a,b,c (none over 2000) evaluate the triplet of its medians m_a , m_b , m_c .
Let those three become sides of a new triangle i.e. (a,b,c) =(m_a , m_b , m_c ).
<end>

It is up to you to find a triplet (a,b,c) such that the above procedure can be executed a maximal number of times, creating sets of “medians“ with integer values only.

The answer should include: (a,b,c) and all interim sets of medians.

Rem: Can be solved analytically.