is this based off the "four is the magic number" game?

in which you start with a random number, say 10, and say "ten is three, three is five, five is four, four is four and four is the magic number"

it seems that a_n = L(a_n-1) always converges to 4 so i guess 4 is the only case where |n| = L(n)

no idea how to prove it though