this is for holding javascript data
Benedict Irwin added Things.tex
over 9 years ago
Commit id: 776cac0157e1d1c19026dc3f52755a16c168b417
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\section{Things}
\begin{equation}
S_n=\lceil\frac{n}{2}\rceil=\sum_i^n i \; \mathrm{mod} \; 2 = 1,1,2,2,3,3,4,4,... \\
S_n^2=\lceil\frac{n}{2}\rceil^2=\sum_i^n i^\alpha \; \mathrm{mod} \; 2i = 1,1,4,4,9,9,16,16... , \forall \alpha > 1 (??) \\
\frac{1}{3}(4\lceil\frac{n}{2}\rceil^3-\lceil\frac{n}{2}\rceil)=\sum_i^n i^3 \; \mathrm{mod} \; 2i^2 = 1,1,10,10,35,35,84,84... \\
\end{equation}
Therefore \begin{equation}
4\lceil\frac{n}{2}\rceil^3=3\sum_i^n i^3 \; \mathrm{mod} \; 2i^2 + \sum_i^n i \; \mathrm{mod} \; 2
\end{equation}
