Pair of Ulam Numbers differing by One

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Open Question

The largest known pair of Ulam numbers which differ by $1$ are $47$ and $48$.

It is not known whether there are any higher.

Historical Note

According to David Wells in his Curious and Interesting Numbers, 2nd ed. of $1997$, the Ulam numbers were investigated up to $20 \, 000$ terms by a P. Muller, whom this contributor has not been able to identify.

Notwithstanding the scarcity of pairs of Ulam numbers which differ by $1$, more than $60\%$ of pairs differ by $2$.