$14 = 3+3+8,\\ 15 = 3+3+3+3+3\\ 16 = 8+8$
For every $n \in \mathbb{Z}^+$ where $n \ge 14$,
$S(n): n$ can be written as sum of 3's and/or 8's
$n_0 = 14, n_1 = 16$
Then, $S(14),S(15),S(16)$ is my base case
But i'm stuck at the next step
The textbook shows
(Inductive Hypothesis for when $k \ge 16$)
$S(14),S(15),\dots,S(k-2),S(k-1)$, and $S(k)$ for some $k \in \mathbb{Z}^+$
Where and why and how is $S(k-2)$ there? and why $k \ge 16$? Shouldn't it be $k > 16$