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| | ==Selected Sequences== | | ==Selected Sequences== |
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| − | {| align="center" border="1" width="90%"
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| − | |+ style="height:25px" | <math>\text{Prime Factorizations, Riffs, and Rotes}\!</math>
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| − | |- style="height:50px; background:#f0f0ff"
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| − | |
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| − | {| cellpadding="12" style="background:#f0f0ff; text-align:center; width:100%"
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| − | | width="10%" | <math>\text{Integer}\!</math>
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| − | | width="25%" | <math>\text{Factorization}\!</math>
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| − | | width="15%" | <math>\text{Notation}\!</math>
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| − | | width="25%" | <math>\text{Riff Digraph}\!</math>
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| − | | width="25%" | <math>\text{Rote Graph}\!</math>
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| − | |}
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| − | |-
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| − | |
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| − | {| cellpadding="12" style="text-align:center; width:100%"
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| − | | width="10%" | <math>1\!</math>
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| − | | width="25%" | <math>1\!</math>
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| − | | width="15%" |
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| − | | width="25%" |
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| − | | width="25%" | [[Image:Rote 1 Big.jpg|20px]]
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| − | |}
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| − | |-
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| − | |
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| − | {| cellpadding="12" style="text-align:center; width:100%"
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| − | | width="10%" | <math>2\!</math>
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| − | | width="25%" | <math>\text{p}_1^1\!</math>
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| − | | width="15%" | <math>\text{p}\!</math>
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| − | | width="25%" | [[Image:Riff 2 Big.jpg|20px]]
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| − | | width="25%" | [[Image:Rote 2 Big.jpg|40px]]
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| − | |}
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| − | |-
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| − | |
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| − | {| cellpadding="12" style="text-align:center; width:100%"
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| − | | width="10%" | <math>3\!</math>
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| − | | width="25%" |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_2^1 & = & \text{p}_{\text{p}_1^1}^1
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| − | \end{array}</math>
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| − | | width="15%" | <math>\text{p}_\text{p}\!</math>
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| − | | width="25%" | [[Image:Riff 3 Big.jpg|40px]]
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| − | | width="25%" | [[Image:Rote 3 Big.jpg|40px]]
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| − | |-
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| − | | <math>4\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^2 & = & \text{p}_1^{\text{p}_1^1}
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| − | \end{array}</math>
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| − | | <math>\text{p}^\text{p}\!</math>
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| − | | [[Image:Riff 4 Big.jpg|40px]]
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| − | | [[Image:Rote 4 Big.jpg|65px]]
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| − | |}
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| − | |-
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| − | |
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| − | {| cellpadding="12" style="text-align:center; width:100%"
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| − | | width="10%" | <math>5\!</math>
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| − | | width="25%" |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_3^1
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| − | & = & \text{p}_{\text{p}_2^1}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_{\text{p}_1^1}^1}^1
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| − | \end{array}</math>
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| − | | width="15%" | <math>\text{p}_{\text{p}_{\text{p}}}\!</math>
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| − | | width="25%" | [[Image:Riff 5 Big.jpg|65px]]
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| − | | width="25%" | [[Image:Rote 5 Big.jpg|40px]]
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| − | |-
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| − | | <math>6\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^1 \text{p}_2^1
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| − | & = & \text{p}_1^1 \text{p}_{\text{p}_1^1}^1
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| − | \end{array}</math>
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| − | | <math>\text{p} \text{p}_{\text{p}}\!</math>
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| − | | [[Image:Riff 6 Big.jpg|65px]]
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| − | | [[Image:Rote 6 Big.jpg|80px]]
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| − | |-
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| − | | <math>7\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_4^1
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| − | & = & \text{p}_{\text{p}_1^2}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_1^{\text{p}_1^1}}^1
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| − | \end{array}</math>
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| − | | <math>\text{p}_{\text{p}^{\text{p}}}\!</math>
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| − | | [[Image:Riff 7 Big.jpg|65px]]
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| − | | [[Image:Rote 7 Big.jpg|65px]]
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| − | |-
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| − | | <math>8\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^3
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| − | & = & \text{p}_1^{\text{p}_2^1}
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| − | \\[12pt]
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| − | & = & \text{p}_1^{\text{p}_{\text{p}_1^1}^1}
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| − | \end{array}</math>
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| − | | <math>\text{p}^{\text{p}_{\text{p}}}\!</math>
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| − | | [[Image:Riff 8 Big.jpg|65px]]
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| − | | [[Image:Rote 8 Big.jpg|65px]]
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| − | |-
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| − | | <math>9\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_2^2
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| − | & = & \text{p}_{\text{p}_1^1}^{\text{p}_1^1}
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| − | \end{array}</math>
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| − | | <math>\text{p}_\text{p}^\text{p}\!</math>
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| − | | [[Image:Riff 9 Big.jpg|40px]]
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| − | | [[Image:Rote 9 Big.jpg|80px]]
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| − | |-
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| − | | <math>16\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^4
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| − | & = & \text{p}_1^{\text{p}_1^2}
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| − | \\[12pt]
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| − | & = & \text{p}_1^{\text{p}_1^{\text{p}_1^1}}
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| − | \end{array}</math>
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| − | | <math>\text{p}^{\text{p}^{\text{p}}}\!</math>
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| − | | [[Image:Riff 16 Big.jpg|65px]]
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| − | | [[Image:Rote 16 Big.jpg|90px]]
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| − | |}
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| − | |-
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| − | |
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| − | {| cellpadding="12" style="text-align:center; width:100%"
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| − | | width="10%" | <math>10\!</math>
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| − | | width="25%" |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^1 \text{p}_3^1
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| − | & = & \text{p}_1^1 \text{p}_{\text{p}_2^1}^1
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| − | \\[12pt]
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| − | & = & \text{p}_1^1 \text{p}_{\text{p}_{\text{p}_1^1}^1}^1
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| − | \end{array}</math>
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| − | | width="15%" | <math>\text{p} \text{p}_{\text{p}_{\text{p}}}\!</math>
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| − | | width="25%" | [[Image:Riff 10 Big.jpg|90px]]
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| − | | width="25%" | [[Image:Rote 10 Big.jpg|80px]]
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| − | |-
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| − | | <math>11\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_5^1
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| − | & = & \text{p}_{\text{p}_3^1}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_{\text{p}_2^1}^1}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_{\text{p}_{\text{p}_1^1}^1}^1}^1
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| − | \end{array}</math>
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| − | | <math>\text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math>
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| − | | [[Image:Riff 11 Big.jpg|90px]]
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| − | | [[Image:Rote 11 Big.jpg|40px]]
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| − | |-
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| − | | <math>12\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^2 \text{p}_2^1
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| − | & = & \text{p}_1^{\text{p}_1^1} \text{p}_{\text{p}_1^1}^1
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| − | \end{array}</math>
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| − | | <math>\text{p}^{\text{p}} \text{p}_{\text{p}}\!</math>
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| − | | [[Image:Riff 12 Big.jpg|65px]]
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| − | | [[Image:Rote 12 Big.jpg|105px]]
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| − | |-
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| − | | <math>13\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_6^1
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| − | & = & \text{p}_{\text{p}_1^1 \text{p}_2^1}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_1^1 \text{p}_{\text{p}_1^1}^1}^1
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| − | \end{array}</math>
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| − | | <math>\text{p}_{\text{p} \text{p}_{\text{p}}}\!</math>
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| − | | [[Image:Riff 13 Big.jpg|65px]]
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| − | | [[Image:Rote 13 Big.jpg|80px]]
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| − | |-
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| − | | <math>14\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^1 \text{p}_4^1
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| − | & = & \text{p}_1^1 \text{p}_{\text{p}_1^2}^1
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| − | \\[12pt]
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| − | & = & \text{p}_1^1 \text{p}_{\text{p}_1^{\text{p}_1^1}}^1
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| − | \end{array}</math>
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| − | | <math>\text{p} \text{p}_{\text{p}^{\text{p}}}\!</math>
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| − | | [[Image:Riff 14 Big.jpg|90px]]
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| − | | [[Image:Rote 14 Big.jpg|105px]]
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| − | |-
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| − | | <math>17\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_7^1
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| − | & = & \text{p}_{\text{p}_4^1}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_{\text{p}_1^2}^1}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_{\text{p}_1^{\text{p}_1^1}}^1}^1
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| − | \end{array}</math>
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| − | | <math>\text{p}_{\text{p}_{\text{p}^{\text{p}}}}\!</math>
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| − | | [[Image:Riff 17 Big.jpg|90px]]
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| − | | [[Image:Rote 17 Big.jpg|65px]]
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| − | |-
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| − | | <math>18\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^1 \text{p}_2^2
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| − | & = & \text{p}_1^1 \text{p}_{\text{p}_1^1}^{\text{p}_1^1}
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| − | \end{array}</math>
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| − | | <math>\text{p} \text{p}_{\text{p}}^{\text{p}}\!</math>
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| − | | [[Image:Riff 18 Big.jpg|65px]]
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| − | | [[Image:Rote 18 Big.jpg|120px]]
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| − | |-
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| − | | <math>19\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_8^1
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| − | & = & \text{p}_{\text{p}_1^3}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_1^{\text{p}_2^1}}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_1^{\text{p}_{\text{p}_1^1}^1}}^1
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| − | \end{array}</math>
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| − | | <math>\text{p}_{\text{p}^{\text{p}_{\text{p}}}}\!</math>
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| − | | [[Image:Riff 19 Big.jpg|90px]]
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| − | | [[Image:Rote 19 Big.jpg|65px]]
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| − | |-
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| − | | <math>23\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_9^1
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| − | & = & \text{p}_{\text{p}_2^2}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_{\text{p}_1^1}^{\text{p}_1^1}}^1
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| − | \end{array}</math>
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| − | | <math>\text{p}_{\text{p}_{\text{p}}^{\text{p}}}\!</math>
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| − | | [[Image:Riff 23 Big.jpg|65px]]
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| − | | [[Image:Rote 23 Big.jpg|80px]]
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| − | |-
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| − | | <math>25\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_3^2
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| − | & = & \text{p}_{\text{p}_2^1}^{\text{p}_1^1}
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_{\text{p}_1^1}^1}^{\text{p}_1^1}
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| − | \end{array}</math>
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| − | | <math>\text{p}_{\text{p}_{\text{p}}}^{\text{p}}\!</math>
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| − | | [[Image:Riff 25 Big.jpg|65px]]
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| − | | [[Image:Rote 25 Big.jpg|80px]]
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| − | |-
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| − | | <math>27\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_2^3
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| − | & = & \text{p}_{\text{p}_1^1}^{\text{p}_2^1}
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_1^1}^{\text{p}_{\text{p}_1^1}^1}
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| − | \end{array}</math>
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| − | | <math>\text{p}_{\text{p}}^{\text{p}_{\text{p}}}\!</math>
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| − | | [[Image:Riff 27 Big.jpg|65px]]
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| − | | [[Image:Rote 27 Big.jpg|80px]]
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| − | |-
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| − | | <math>32\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^5
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| − | & = & \text{p}_1^{\text{p}_3^1}
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| − | \\[12pt]
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| − | & = & \text{p}_1^{\text{p}_{\text{p}_2^1}^1}
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| − | \\[12pt]
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| − | & = & \text{p}_1^{\text{p}_{\text{p}_{\text{p}_1^1}^1}^1}
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| − | \end{array}</math>
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| − | | <math>\text{p}^{\text{p}_{\text{p}_{\text{p}}}}\!</math>
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| − | | [[Image:Riff 32 Big.jpg|90px]]
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| − | | [[Image:Rote 32 Big.jpg|65px]]
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| − | |-
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| − | | <math>49\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_4^2
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| − | & = & \text{p}_{\text{p}_1^2}^{\text{p}_1^1}
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_1^{\text{p}_1^1}}^{\text{p}_1^1}
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| − | \end{array}</math>
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| − | | <math>\text{p}_{\text{p}^{\text{p}}}^{\text{p}}\!</math>
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| − | | [[Image:Riff 49 Big.jpg|65px]]
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| − | | [[Image:Rote 49 Big.jpg|80px]]
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| − | |-
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| − | | <math>53\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_{16}^1
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| − | & = & \text{p}_{\text{p}_1^4}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_1^{\text{p}_1^2}}^1
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_1^{\text{p}_1^{\text{p}_1^1}}}^1
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| − | \end{array}</math>
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| − | | <math>\text{p}_{\text{p}^{\text{p}^{\text{p}}}}\!</math>
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| − | | [[Image:Riff 53 Big.jpg|90px]]
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| − | | [[Image:Rote 53 Big.jpg|90px]]
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| − | |-
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| − | | <math>64\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^6
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| − | & = & \text{p}_1^{\text{p}_1^1 \text{p}_2^1}
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| − | \\[12pt]
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| − | & = & \text{p}_1^{\text{p}_1^1 \text{p}_{\text{p}_1^1}^1}
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| − | \end{array}</math>
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| − | | <math>\text{p}^{\text{p} \text{p}_{\text{p}}}\!</math>
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| − | | [[Image:Riff 64 Big.jpg|65px]]
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| − | | [[Image:Rote 64 Big.jpg|105px]]
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| − | |-
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| − | | <math>81\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_2^4
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| − | & = & \text{p}_{\text{p}_1^1}^{\text{p}_1^2}
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| − | \\[12pt]
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| − | & = & \text{p}_{\text{p}_1^1}^{\text{p}_1^{\text{p}_1^1}}
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| − | \end{array}</math>
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| − | | <math>\text{p}_{\text{p}}^{\text{p}^{\text{p}}}\!</math>
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| − | | [[Image:Riff 81 Big.jpg|65px]]
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| − | | [[Image:Rote 81 Big.jpg|105px]]
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| − | |-
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| − | | <math>128\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^7
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| − | & = & \text{p}_1^{\text{p}_4^1}
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| − | \\[12pt]
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| − | & = & \text{p}_1^{\text{p}_{\text{p}_1^2}^1}
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| − | \\[12pt]
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| − | & = & \text{p}_1^{\text{p}_{\text{p}_1^{\text{p}_1^1}}^1}
| |
| − | \end{array}</math>
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| − | | <math>\text{p}^{\text{p}_{\text{p}^{\text{p}}}}\!</math>
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| − | | [[Image:Riff 128 Big.jpg|90px]]
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| − | | [[Image:Rote 128 Big.jpg|90px]]
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| − | |-
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| − | | <math>256\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^8
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| − | & = & \text{p}_1^{\text{p}_1^3}
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| − | \\[12pt]
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| − | & = & \text{p}_1^{\text{p}_1^{\text{p}_2^1}}
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| − | \\[12pt]
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| − | & = & \text{p}_1^{\text{p}_1^{\text{p}_{\text{p}_1^1}^1}}
| |
| − | \end{array}</math>
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| − | | <math>\text{p}^{\text{p}^{\text{p}_{\text{p}}}}\!</math>
| |
| − | | [[Image:Riff 256 Big.jpg|90px]]
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| − | | [[Image:Rote 256 Big.jpg|90px]]
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| − | |-
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| − | | <math>512\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^9
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| − | & = & \text{p}_1^{\text{p}_2^2}
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| − | \\[12pt]
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| − | & = & \text{p}_1^{\text{p}_{\text{p}_1^1}^{\text{p}_1^1}}
| |
| − | \end{array}</math>
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| − | | <math>\text{p}^{\text{p}_{\text{p}}^{\text{p}}}\!</math>
| |
| − | | [[Image:Riff 512 Big.jpg|65px]]
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| − | | [[Image:Rote 512 Big.jpg|105px]]
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| − | |-
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| − | | <math>65536\!</math>
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| − | |
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| − | <math>\begin{array}{lll}
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| − | \text{p}_1^{16}
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| − | & = & \text{p}_1^{\text{p}_1^4}
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| − | \\[12pt]
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| − | & = & \text{p}_1^{\text{p}_1^{\text{p}_1^2}}
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| − | \\[12pt]
| |
| − | & = & \text{p}_1^{\text{p}_1^{\text{p}_1^{\text{p}_1^1}}}
| |
| − | \end{array}</math>
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| − | | <math>\text{p}^{\text{p}^{\text{p}^{\text{p}}}}\!</math>
| |
| − | | [[Image:Riff 65536 Big.jpg|90px]]
| |
| − | | [[Image:Rote 65536 Big.jpg|115px]]
| |
| − | |}
| |
| − | |}
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| | | | |
| | ===A061396=== | | ===A061396=== |
