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.