Let us see if I understand your question:
Let "n" be a positive integer. I will choose "n" to be = 4. So, 2^n = 2^4 =16, and 16 mod 13 =3. And let "k" be the number of positive integers LESS than 2^4 or 16. In other words, "k" will range from 1 to 15. So, the question is: what is the remainder when"k" is divided by 13? Well, if "k" is from 1 to 15, then you have the following:
1 mod 13 = 1 - the remainder
2 mod 13 = 2 - the remainder
3 mod 13 = 3 - the remainder.
4 mod 13 = 4 - the remainder.
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13 mod 13 = 0
14 mod 13 = 1 - the remainder
15 mod 13 = 2 -the remainder. And so on. And this pattern will continue for any "n" you choose.
And that is the way I read it!