I've worked it out, and now I'm not sure that this function is OEIS-worthy (although it's at least as worthy as Jenny's constant). I will definitely post a question on Math StackExchange, and not answer it (if even necessary) for a month or two, in honor of my namesake.
Here is a link to the question.
Here is a link to a related question that is more fun.
This is the supposedly-bimonthly-but-we-keep-skipping 'What are you working On?' thread. Previous threads are here. So here's the question:
What are you working on?
Here are some guidelines: