2017 AMC 12A Problems/Problem 7
Problem
Define a function on the positive integers recursively by 
, 
if 
is even, and 
if is odd and greater than 
. What is 
?
Solution
This is a recursive function, which means the function is used to evaluate itself. To solve this, we must identify the base case, 
. We also know that when is odd, 
. Thus we know that 
. Thus we know that n will always be odd in the recursion of , and we add 
each recursive cycle, which there are 
of. Thus the answer is 
, which is answer
.
Note that when you write out a few numbers, you find that 
for any , so 
See Also
| 2017 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 6 |
Followed by Problem 8 |
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| All AMC 12 Problems and Solutions | |
