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Directory:Jon Awbrey/Papers/Riffs and Rotes (view source)
Revision as of 15:30, 25 January 2010
, 15:30, 25 January 2010→A061396
* [http://oeis.org/wiki/A061396 OEIS Wiki Entry for A061396].
* [http://oeis.org/wiki/A061396 OEIS Wiki Entry for A061396].
{| align="center" border="1" width="96%"
|+ style="height:24px" | <math>\text{Prime Factorizations, Riffs, Rotes, and Traversals}\!</math>
|- style="height:50px; background:#f0f0ff"
|
{| cellpadding="12" style="background:#f0f0ff; text-align:center; width:100%"
| width="10%" | <math>\text{Integer}\!</math>
| width="19%" | <math>\text{Factorization}\!</math>
| width="14%" | <math>\text{Notation}\!</math>
| width="19%" | <math>\text{Riff Digraph}\!</math>
| width="19%" | <math>\text{Rote Graph}\!</math>
| width="19%" | <math>\text{Traversal}\!</math>
|}
|-
|
{| cellpadding="12" style="text-align:center; width:100%"
| width="10%" | <math>1\!</math>
| width="19%" | <math>1\!</math>
| width="14%" |
| width="19%" |
| width="19%" | [[Image:Rote 1 Big.jpg|20px]]
| width="19%" |
|}
|-
|
{| cellpadding="12" style="text-align:center; width:100%"
| width="10%" | <math>2\!</math>
| width="19%" | <math>\text{p}_1^1\!</math>
| width="14%" | <math>\text{p}\!</math>
| width="19%" | [[Image:Riff 2 Big.jpg|20px]]
| width="19%" | [[Image:Rote 2 Big.jpg|40px]]
| width="19%" | <math>((~))</math>
|}
|-
|
{| cellpadding="12" style="text-align:center; width:100%"
| width="10%" | <math>3\!</math>
| width="19%" |
<math>\begin{array}{lll}
\text{p}_2^1 & = & \text{p}_{\text{p}_1^1}^1
\end{array}</math>
| width="14%" | <math>\text{p}_\text{p}\!</math>
| width="19%" | [[Image:Riff 3 Big.jpg|40px]]
| width="19%" | [[Image:Rote 3 Big.jpg|40px]]
| width="19%" | <math>(((~))(~))</math>
|-
| <math>4\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^2 & = & \text{p}_1^{\text{p}_1^1}
\end{array}</math>
| <math>\text{p}^\text{p}\!</math>
| [[Image:Riff 4 Big.jpg|40px]]
| [[Image:Rote 4 Big.jpg|65px]]
| <math>((((~))))</math>
|}
|-
|
{| cellpadding="12" style="text-align:center; width:100%"
| width="10%" | <math>5\!</math>
| width="19%" |
<math>\begin{array}{lll}
\text{p}_3^1
& = & \text{p}_{\text{p}_2^1}^1
\\[10pt]
& = & \text{p}_{\text{p}_{\text{p}_1^1}^1}^1
\end{array}</math>
| width="14%" | <math>\text{p}_{\text{p}_{\text{p}}}\!</math>
| width="19%" | [[Image:Riff 5 Big.jpg|65px]]
| width="19%" | [[Image:Rote 5 Big.jpg|40px]]
| width="19%" | <math>((((~))(~))(~))</math>
|-
| <math>6\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^1 \text{p}_2^1
& = & \text{p}_1^1 \text{p}_{\text{p}_1^1}^1
\end{array}</math>
| <math>\text{p} \text{p}_{\text{p}}\!</math>
| [[Image:Riff 6 Big.jpg|65px]]
| [[Image:Rote 6 Big.jpg|80px]]
| <math>((~))(((~))(~))</math>
|-
| <math>7\!</math>
|
<math>\begin{array}{lll}
\text{p}_4^1
& = & \text{p}_{\text{p}_1^2}^1
\\[10pt]
& = & \text{p}_{\text{p}_1^{\text{p}_1^1}}^1
\end{array}</math>
| <math>\text{p}_{\text{p}^{\text{p}}}\!</math>
| [[Image:Riff 7 Big.jpg|65px]]
| [[Image:Rote 7 Big.jpg|65px]]
| <math>(((((~))))(~))</math>
|-
| <math>8\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^3
& = & \text{p}_1^{\text{p}_2^1}
\\[10pt]
& = & \text{p}_1^{\text{p}_{\text{p}_1^1}^1}
\end{array}</math>
| <math>\text{p}^{\text{p}_{\text{p}}}\!</math>
| [[Image:Riff 8 Big.jpg|65px]]
| [[Image:Rote 8 Big.jpg|65px]]
| <math>(((((~))(~))))</math>
|-
| <math>9\!</math>
|
<math>\begin{array}{lll}
\text{p}_2^2
& = & \text{p}_{\text{p}_1^1}^{\text{p}_1^1}
\end{array}</math>
| <math>\text{p}_\text{p}^\text{p}\!</math>
| [[Image:Riff 9 Big.jpg|40px]]
| [[Image:Rote 9 Big.jpg|80px]]
| <math>(((~))(((~))))</math>
|-
| <math>16\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^4
& = & \text{p}_1^{\text{p}_1^2}
\\[10pt]
& = & \text{p}_1^{\text{p}_1^{\text{p}_1^1}}
\end{array}</math>
| <math>\text{p}^{\text{p}^{\text{p}}}\!</math>
| [[Image:Riff 16 Big.jpg|65px]]
| [[Image:Rote 16 Big.jpg|90px]]
| <math>((((((~))))))</math>
|}
|}
===A062504===
===A062504===