, 2022

If $a$ is odd, the output is
$a+3$, which is even because it is
the sum of two odd integers.

If $a$ is even, the output is $a+5$, which is odd, because it is the sum
of an even integer and an odd integer.

Starting with $a=15$ and using the
machine 2 times, we obtain $15 $\to$ 15 + 3 =
18 $\to$ 18 + 5 = 23$.

Starting with 23 and using the machine 2 times, we obtain $23 \to 23 + 3 = 26 \to 26 + 5 = 31$.

Starting with an odd integer and using the machine 2 times, the net
result is adding 8 to the input, because the odd input generates a first
output that is 3 larger (and so even) and a second output that is 5
larger than the first output.

This generates a net result that is $3+5$ larger than the input.

Therefore, using the machine 46 more times (that is, repeating the 2
steps a total of 23 more times), we add 8 a total of 23 more times to
obtain the output $31 + 23 $\cdot$ 8 =
215$.

To this point, the machine has been used 50 times.

Using the machine for the 51st time, $215 $\to$
215 + 3 = 218$ and so the final output is 218.