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 $15 \rightarrow 15+3=18 \rightarrow 18+5=23$. Starting with 23 and using the machine 2 times, we obtain $23 \rightarrow 23+3=26 \rightarrow 26+5=31$. 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, $215 \rightarrow 215+3=218$ and so the final output is 218.