Help needed for Math Problems

Question

Starting with the number 0 on my calculator, I do a calculation in 5 steps. At each step, I either add 1 or multiply by 2. What is the smallest number that cannot be the final result?

Answer 1

The set of numbers that can be obtained by adding 1 or multiplying by 2 from 0 is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, ...}.

The first number that cannot be obtained using this process is 11. All numbers greater than or equal to 11 can be reached using the given steps, but 11 cannot be reached by adding 1 or multiplying by 2 from 0 in 5 steps.