# Calculator Keystrokes

Tyler has two calculators, both of which initially display zero. The first calculator has only two buttons, $$[+1]$$ and $$[\times 2]$$. The second has only the buttons $$[+1]$$ and $$[\times 4]$$. Both calculators update their displays immediately after each keystroke.

A positive integer $$n$$ is called ambivalent if the minimum number of keystrokes needed to display $$n$$ on the first calculator equals the minimum number of keystrokes needed to display $$n$$ on the second calculator. Find the last three digits of the $$2014^\text{th}$$ smallest ambivalent number.

×