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Density of odd numbers in a sequence relating base 2 and base 3 expansion
Define the function
$$f(4n)=6n+1\\
f(4n+1)=6n+2\\
f(4n+2)=6n+3\\
f(4n+3)=6n+5$$
and the sequence $u_0=2$, $u_{k+1}=f(u_k)$.
Let $d_1\le d_2$ be the lower and upper asymptotic density of odd numbers ...
