Is there any limit to how many times you can increase velocity by repeated sling shot manoeuvres? and its answers have got me thinking, and that's always dangerous.
Suppose you have a durable RTG-powered spacecraft launched from Earth, and your goal is to use Jupiter-only flybys as many times as you can in order to set some sort of record before going off to explore some place further.
We've got to put some constrains on what a "flyby" is otherwise you'd just go into a 5.2 AU heliocentric retrograde orbit and pick up 16 conjunctions per century and call them "distant perturbative flybys".
So to be a flyby, the heliocentric characteristic energy $C_3$ and/or the semimajor axis $a$ have to increase by some factor.
I'll call that factor 10% arbitrarily. If there are profound or compelling answers that have a slightly lower factor they won't be balked-at :-)
Flybys for primarily inclination changes should obtain a similar delta-v to those above in order to count.
Question: This is a flyby puzzler; starting from Earth, how many times can you use Jupiter flybys in one century?