Visualizing the Gilbreath expectation sequence

One byproduct of learning how to use coding agents to create visualization apps is that it now becomes straightforward to convert any figure in one’s papers that had already been generated by code (e.g., in Python) into a more interactive, animated applet. I can illustrate this with Figure 1 from my recent paper on the Gilbreath conjecture with Chase and Hunter, reproduced below: This plot displays both exact and numerically simulated values of a certain poorly understood sequence relating to the Gilbreath conjecture, which I will call the “Gilbreath expectation sequence” here for lack of a better name. The definition of the sequence is as follows. Consider a “Gilbreath array” which is an inverted pyramid, where the top entries are independent exponential random variables of mean 1, and all the other entries are the absolute values of the differences of the two entries immediately above it. Thanks to the visualizer app, I can quickly give an example (with ): The left diagonal entries…