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Benedict Irwin added Base 10 Master Seq.tex
over 9 years ago
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\section{Base 10 Master Sequences}
For the last digit, if this sequence can define the whole chain by modular arithmetic, there are 4 digit sequences in base 10 \begin{equation}
0: \;0000 \\
1: \;1111 \\
2: \;2486 \\
3: \;3971 \\
4: \;4646 \\
5: \;5555 \\
6: \;6666 \\
7: \;7931 \\
8: \;8426 \\
9: \;9191 \\
0: \;0000 \\
\end{equation}
Here we can see that the pairs $2$ and $8$, and $3$ and $7$ both use the same digits, but in a different order. Certain pairs, when "folded", that is the last two digits summmed on to the respective of the first two digits, form $0000$. These pairs are, $0,2,3,5,7,8,0$. Denote these $f-pairs$.Then there are pairs where if the last two digits are swapped and then the fold is made they sum to $0000$, these are $4$ and $9$., denote these $s-pairs$. Then we have $f,.,f,f,.,f,.,f,f,.,f$, a symmetric sequence, where $.$ means not an $f-pair$.
