Even funner fact: digging into the OAI proof to see what it actually says, quantitatively...
looking at terms of size ~ n^{-0.2}
Can't be more than 15,000 of them...for n growing exponentially. Need to go up to at least 10^{2,900,000,000} terms before it has anything to say...
Fun fact: it is known that the Flint-Hills series converges
Σₙ 1/(n³sin²n)