**NOTATION**: $O_x$ -- the product of all odd primes $\le x$.

E.g. $O_7=3\cdot 5\cdot 7 = 105$.

**QUESTION**: Are the three ordered pairs $\ (d\ p)=(1\ 3)\ \ (2\ 3)\ \ (4\ 5)\ $ the only solutions of the equation:
$$|O_p-2^d|=1$$
in natural numbers $d$, and odd primes $p$?

(I don't know an answer).

**MOTIVATION**: Let $\ s\ $ be a prime just after $\ p$, so that $\ p<s$. If
$$|O_p-2^d|\ne 1$$
then
$$|O_p-2^d|\ge s$$
Furthermore, sometimes $\ s\ $ can be quite a bit larger than $\ p$.

**ACKNOWLEDGEMENT**: Bjørn Kjos-Hanssen has provided one of the above solutions (see his answer below).

similar interesting" seems vague and too encompassing). – Włodzimierz Holsztyński Apr 12 '14 at 19:07