I am not sure if this qualifies, but Mitchell Feigenbaum used an HP-65 calculator to discover the Feigenbaum constant and used the insights he gained from his calculations to write Quantitative Universality for a Class of Nonlinear Transformations.

In a similar way, Stephen Wolfram's computational experiments with Cellular Automata led him to work that culminated in his book A New Kind of Science. These two people were Physicists, but the results that they came up with are purely mathematical.