Benedict Irwin edited Base 10 Master Seq.tex  over 9 years ago

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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}