Even in the 1950s, my mother worked on a machine that could be programmed in octal, but you could change the instruction set with patch cables.
The transition period where patch cables and stored programs coexisted is one of the most interesting eras in computing history.
I kind of think she was at White Sands at the time, so... maybe look at what White Sands was using for missile trajectory calculations around 1954 or 1955?