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## 'What a Coincidence!' printed from http://nrich.maths.org/

The sequences have common differences of $7$ and $9$ respectively.

The lowest common multiple of $7$ and $9$ is $63$, so the next term after $2005$ to appear in both sequences is $2005 + 63$, that is $2068$.

*This problem is taken from the UKMT Mathematical Challenges.*