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Benedict Irwin edited The 21 thing.tex
over 9 years ago
Commit id: 5d518cb8b3804680a3d21d03f0c2df4b8d31a977
deletions | additions
diff --git a/The 21 thing.tex b/The 21 thing.tex
index c265b6f..b8bbeb5 100644
--- a/The 21 thing.tex
+++ b/The 21 thing.tex
...
Find $(21;;n)$ primality, \begin{equation}
\begin{array}{|c|c|c|}
\hline
n & prime? & fact
\\ & rewrite\\
\hline
(21;;1) & 0 & 3×7
& (21;;1) \\
(21;;2) & 0 & 3×7×101
\\ & (21;;1)×101\\
(21;;3) & 0 & 3^2×7^2×13×37
\\ &(21;;1)^2×13×37\\
(21;;4) & 0 & 3×7×73×101×137
\\ &(21;;2)×73×137\\
(21;;5) & 0 & 3×7×41×271×9091
\\ &\\
(21;;6) & 0 & 3^2×7^2×13×37×101×9901
\\ & \frac{(21;;2)×(21;;3)×9901}{(21;;1)}\\
(21;;7) & 0 & 3×7×239×4649×909091 \\
(21;;8) & 0 & 3×7×17×73×101×137×5882353 \\
(21;;9) & 0 & 3^3×7^2×13×19×37×52579×333667 \\
...
\end{array}
\end{equation}
Each sequence seems individual and fascinating. Everything seems to have a factor of $3$,$7$. However our old friends $9091$ and $9901$ appear very soon into the sequence at $n=5,6$, funnily enough begin $10,12$ divided by two, which were the $11...$ sequences positions. Also $5882353$ makes an appearence at $8$ which is $16$ by two, $16$ begin the $111...$ sequence counterpart.
Equally our friend \begin{equation}
9901 = \frac{(21;;1)(21;;6)}{(21;;2)(21;;3)}
\end{equation}