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I've read that the sequence $\left(e_n\right)_{n \in \mathbb{N}}$ $$ e_0=1\text{ and } \ e_n=e_{\left\lfloor \,n/2 \right\rfloor}+e_{\left\lfloor \,n/3 \right\rfloor}+e_{\left\lfloor \,n/6 \right\rfloor} $$ satisfies the beautiful equality $$ \frac{e_n}{n} \underset{n \rightarrow +\infty}{\rightarrow}\frac{12}{\ln\left(432\right)} $$ I read the proof of Erdös himself but he proves the general case. Is there an easier way to prove this equality ? I would be curious to see it !

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marked as duplicate by Rohan, steven gregory, Daniel Fischer sequences-and-series Jan 16 '18 at 14:20

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