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Benedict Irwin edited Base 10 Master Seq.tex
over 9 years ago
Commit id: a75d625de215a31d565c91b109677a72f15514d4
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\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 $f-pair$.
Base 1:
Base 2: \begin{equation}
0: \; 0000 \\
1: \; 1111 \\
2: \; 0000 \\
3: \; 1111 \\
4: \; 0000 \\
5: \; 1111 \\
6: \; 0000 \\
\end{equation}
Base 3: \begin{equation}
0: \; 0000 \\
1: \; 1111 \\
2: \; 2121 \\
3: \; 0000 \\
4: \; 1111 \\
\end{equation}
Base 4: \begin{equation}
0: \; 0000 \\
1: \; 1111 \\
2: \; 2000 \\
\end{equation}