PASCAL 2023 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, and 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?