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 two each recursive cycle, which there are
of. Thus the answer is