Solving a math problem with planner programming

The blog explains how to solve the following problem using Picat and planner programming, a form of logic programming:

Suppose that at the beginning there is a blank document, and a letter "a" is written in it. In the following steps, only the three functions of "select all", "copy" and "paste" can be used.

Find the minimum number of steps to reach at least 100,000 a's (each of the three operations of "select all", "copy" and "paste" is counted as one step). If the target number is not specified, and I want to get the exact amount of "a"s, is there a general formula?

- Math Stack Exchange