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Dan_Moore comments on What are you working on? October 2013 - Less Wrong
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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.