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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Does the set of happy numbers have a limiting density?

The answer is almost certainly that the limiting density does not exist. Without going into the details of the proof allow me to give a heuristic argument which is based on how the OP likely generated …
Justin Gilmer's user avatar