# Pair of Ulam Numbers differing by One

Jump to navigation
Jump to search

## 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

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $47$