examday

/TMUA

The sequence with $n$th term $u_n=2^n-1$ can be generated by starting with $1$ and repeatedly doubling the previous term and adding $1$.

A student generates a list starting with $1$, but uses each of the following incorrect rules exactly once, at two different steps:

• double the previous number and add $3$;
• double the previous number and subtract $1$.

At every other step, the student doubles the number just obtained and adds $1$.

The tenth number in the student's list is $1047$. What is the first incorrect number in the list?