You could put the Arduino in deep sleep, if you wanted to and that LED will still blink. With a little work, you could probably adapt this idea to any number of circuits out of the 555 playbook ...

[John]’s build is just an Arduino and LCD shield that writes the number 170 to memory on one pass, and the number 85 on the next pass. Because these numbers are 10101010 and 01010101 in binary ...