Greatest $n$ such that $n$ and $n+1$ are Hamming numbers

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As we know, Hamming numbers are numbers with all prime factors $\leq 5$. How can we determine the greatest $n$ such that $n$ and $n+1$ are Hamming numbers? If there is such an $n$....

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The sequence $A085152$ in the OEIS gives all the numbers $n $ such that $n $ and $n+1$ have prime factors $\leq 5$, that is, are Hamming numbers.


Hope it helps.