The primorial $(\#)$ function is defined as the product of first $n$ prime numbers. Is there a simple explanation for the observation that the length of the Collatz sequence for successive primorials increases linearly with $\log{\# (n)}$?
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2Didn't check yet, but I suspect a behaviour like here: https://math.stackexchange.com/questions/2412846/what-causes-this-apparent-pattern-in-hailstone-sequences/2413040 – Collag3n Apr 18 '20 at 11:47