Explain this:

var k = 1
f(x) = 3x+1

Do this:
k = f(x)
k = f(x)
k = f(x)
...
take the digit sum of the digit sum of the digit sum...

It's always 4.


Examples:
1 digit sum 1

4 digit sum 4

13 digit sum 4

40 digit sum 4

121 digit sum 4

364 digit sum 13
13 digit sum 4

1093 digit sum 13
13 digit sum 4

3280 digit sum 13
13 digit sum 4

9841 digit sum 22
22 digit sum 4

29524 digit sum 22
22 digit sum 4
...