deletions | additions       diff --git a/untitled.tex b/untitled.tex  index c004d04..1772e55 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
a_k = 2^k\\  a_{k-1} = -k2^{k-1} \\  a_{k-2} = k(k+3)2^{k-3} \\  a_{k-4} a_{k-3}  = \frac{1}{3}(k(38+k(k+9))2^(k-4)) \\ a_{k-5} a_{k-4}  = \frac{1}{3}(378+179k+18k^2+k^3)2^(k-7)) \\ a_{k-6} a_{k-5}  = \frac{1}{15}(k(9864+k(3030+k(515+k(30+k))))2^(k-8)) \\ \end{equation}  However we must shift the series along to deal with the fact that $S_k(n)$ has $k$ terms, and we end up with \begin{equation}  a_k = 4\cdot2^{k-2}\\  a_{k-1} = -(k-1)2^{k-3} \\  a_{k-2} = (k-2)(k+1)2^{k-5} \\  a_{k-3} = \frac{1}{3}((k-3)(38+(k-3)((k-3)+9))2^(k-7))  \end{equation}  The we can see that the power of $2$ always seems to contain the next prime.