MathDB
Recursive Function

Source: AMC 12A Problem 7

February 8, 2017
AMCAMC 12function2017 AMC 12A

Problem Statement

Define a function on the positive integers recursively by f(1)=2f(1) = 2, f(n)=f(n1)+1f(n) = f(n-1) + 1 if nn is even, and f(n)=f(n2)+2f(n) = f(n-2) + 2 if nn is odd and greater than 11. What is f(2017)f(2017)?
<spanclass=latexbold>(A)</span>2017<spanclass=latexbold>(B)</span>2018<spanclass=latexbold>(C)</span>4034<spanclass=latexbold>(D)</span>4035<spanclass=latexbold>(E)</span>4036<span class='latex-bold'>(A) </span> 2017 \qquad <span class='latex-bold'>(B) </span> 2018 \qquad <span class='latex-bold'>(C) </span> 4034 \qquad <span class='latex-bold'>(D) </span> 4035 \qquad <span class='latex-bold'>(E) </span> 4036