Pair of Ulam Numbers differing by One

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 $2$.


Sources

  • 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.)
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $47$
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