2023 Pascal Problem 21

Starting with a positive integer m, Alicia creates a sequence by applying the following algorithm:

- Step 1: Alicia writes down the number m as the first term of the sequence. - Step 2: If m is even, Alicia sets n = \frac{1}{2}m. If m is odd, Alicia sets n = m + 1. - Step 3: Alicia writes down the number m+n+1 as the next term of the sequence. - Step 4: Alicia sets m equal to the value of the term that she just wrote down in Step 3. - Step 5: Alicia repeats Steps 2, 3, 4 until she has five terms, at which point she stops.

For example, starting with m = 1, Alicia's sequence would be 1, 4, 7, 16, 25. Alicia starts a sequence with m = 3. What is the fifth term of her sequence?

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.