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User:Jon Awbrey/SEQUENCES (view source)

Revision as of 08:33, 11 January 2010

5,755 bytes added ,  08:33, 11 January 2010
→‎A106177
Line 1,357: Line 1,357:  
<p><math>a(6) ~=~ 30</math></p>
 
<p><math>a(6) ~=~ 30</math></p>
 
|}
 
|}
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==A106177==
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* [http://oeis.org/wiki/A106177 A106177]
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 +
===Primal Codes of Finite Partial Functions on Positive Integers===
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{| align="center"
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|
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<math>\begin{array}{rcl}
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1 & = & \varnothing \\
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2 & = & 1\!:\!1 \\
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3 & = & 2\!:\!1 \\
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4 & = & 1\!:\!2 \\
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5 & = & 3\!:\!1 \\
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6 & = & 1\!:\!1 ~~ 2\!:\!1 \\
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7 & = & 4\!:\!1 \\
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8 & = & 1\!:\!3 \\
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9 & = & 2\!:\!2 \\
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10 & = & 1\!:\!1 ~~ 3\!:\!1 \\
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11 & = & 5\!:\!1 \\
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12 & = & 1\!:\!2 ~~ 2\!:\!1 \\
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13 & = & 6\!:\!1 \\
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14 & = & 1\!:\!1 ~~ 4\!:\!1 \\
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15 & = & 2\!:\!1 ~~ 3\!:\!1 \\
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16 & = & 1\!:\!4 \\
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17 & = & 7\!:\!1 \\
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18 & = & 1\!:\!1 ~~ 2\!:\!2 \\
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19 & = & 8\!:\!1 \\
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20 & = & 1\!:\!2 ~~ 3\!:\!1
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\end{array}</math>
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|}
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===Wiki Table===
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{| align="center" style="font-weight:bold; text-align:center"
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| || || || || || || || ||
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| <font color="red">1</font>
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|
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| <font color="red">1</font>
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|-
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| || || || || || || ||
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| <font color="red">2</font>
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| || 1 ||
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| <font color="red">2</font>
 +
|-
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| || || || || || ||
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| <font color="red">3</font>
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| || 1 || || 1 ||
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| <font color="red">3</font>
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|-
 +
| || || || || ||
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| <font color="red">4</font>
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| || 1 || || 2 || || 1 ||
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| <font color="red">4</font>
 +
|-
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| || || || ||
 +
| <font color="red">5</font>
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| || 1 || || 3 || || 1 || || 1 ||
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| <font color="red">5</font>
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|-
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| || || ||
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| <font color="red">6</font>
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| || 1 || || 1 || || 1 || || 4 || || 1 ||
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| <font color="red">6</font>
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|-
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| || ||
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| <font color="red">7</font>
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| || 1 || || 5 || || 2 || || 9 || || 1 || || 1 ||
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| <font color="red">7</font>
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|-
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| ||
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| <font color="red">8</font>
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| || 1 || || 6 || || 1 || || 1 || || 1 || || 2 || || 1 ||
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| <font color="red">8</font>
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|-
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|
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| <font color="red">9</font>
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| || 1 || || 7 || || 1 || || 25|| || 1 || || 3 || || 1 || || 1 ||
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| <font color="red">9</font>
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|-
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| width="12pt" | <font color="red">10</font>
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| width="12pt" |
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| width="12pt" | 1
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| width="12pt" |
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| width="12pt" | 1
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| width="12pt" |
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| width="12pt" | 1
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| width="12pt" |
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| width="12pt" | 36
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| width="12pt" |
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| width="12pt" | 1
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| width="12pt" |
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| width="12pt" | 2
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| width="12pt" |
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| width="12pt" | 1
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| width="12pt" |
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| width="12pt" | 8
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| width="12pt" |
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| width="12pt" | 1
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| width="12pt" |
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| width="12pt" | <font color="red">10</font>
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|}
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===Wiki + TeX===
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====Smallmatrix====
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{| align="center"
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|
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<math>\begin{smallmatrix}
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& & & & & & & & & {\color{red}1} & & {\color{red}1}
 +
\\
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& & & & & & & & {\color{red}2} & & 1 & & {\color{red}2}
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\\
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& & & & & & & {\color{red}3} & & 1 & & 1 & & {\color{red}3}
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\\
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& & & & & & {\color{red}4} & & 1 & & 2 & & 1 & & {\color{red}4}
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\\
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& & & & & {\color{red}5} & & 1 & & 3 & & 1 & & 1 & & {\color{red}5}
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\\
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& & & & {\color{red}6} & & 1 & & 1 & & 1 & & 4 & & 1 & & {\color{red}6}
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\\
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& & & {\color{red}7} & & 1 & & 5 & & 2 & & 9 & & 1 & & 1 & & {\color{red}7}
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\\
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& & {\color{red}8} & & 1 & & 6 & & 1 & & 1 & & 1 & & 2 & & 1 & & {\color{red}8}
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\\
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& {\color{red}9} & & 1 & & 7 & & 1 & & 25 & & 1 & & 3 & & 1 & & 1 & & {\color{red}9}
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\\
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{\color{red}10} & & 1 & & 1 & & 1 & & 36 & & 1 & & 2 & & 1 & & 8 & & 1 & & {\color{red}10}
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\end{smallmatrix}</math>
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|}
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 +
====Array====
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{| align="center"
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|
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<math>\begin{array}{*{21}{c}}
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& & & & & & & & & {\color{red}1} & & {\color{red}1}
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\\
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& & & & & & & & {\color{red}2} & & 1 & & {\color{red}2}
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\\
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& & & & & & & {\color{red}3} & & 1 & & 1 & & {\color{red}3}
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\\
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& & & & & & {\color{red}4} & & 1 & & 2 & & 1 & & {\color{red}4}
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\\
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& & & & & {\color{red}5} & & 1 & & 3 & & 1 & & 1 & & {\color{red}5}
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\\
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& & & & {\color{red}6} & & 1 & & 1 & & 1 & & 4 & & 1 & & {\color{red}6}
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\\
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& & & {\color{red}7} & & 1 & & 5 & & 2 & & 9 & & 1 & & 1 & & {\color{red}7}
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\\
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& & {\color{red}8} & & 1 & & 6 & & 1 & & 1 & & 1 & & 2 & & 1 & & {\color{red}8}
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\\
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& {\color{red}9} & & 1 & & 7 & & 1 & & 25 & & 1 & & 3 & & 1 & & 1 & & {\color{red}9}
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\\
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{\color{red}10} & & 1 & & 1 & & 1 & & 36 & & 1 & & 2 & & 1 & & 8 & & 1 & & {\color{red}10}
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\end{array}</math>
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|}
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====Matrix====
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{| align="center"
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|
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<math>\begin{matrix}
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n \circ m
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\\
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1 ~/~\backslash~ 1
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\\
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2 ~/~ 1 ~\backslash~ 2
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\\
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3 ~/~ 1 \cdot 1 ~\backslash~ 3
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\\
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4 ~/~ 1 \cdot 2 \cdot 1 ~\backslash~ 4
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\\
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5 ~/~ 1 \cdot 3 \cdot 1 \cdot 1 ~\backslash~ 5
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\\
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6 ~/~ 1 \cdot 1 \cdot 1 \cdot 4 \cdot 1 ~\backslash~ 6
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\\
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7 ~/~ 1 \cdot 5 \cdot 2 \cdot 9 \cdot 1 \cdot 1 ~\backslash~ 7
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\\
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8 ~/~ 1 \cdot 6 \cdot 1 \cdot 1 \cdot 1 \cdot 2 \cdot 1 ~\backslash~ 8
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\\
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9 ~/~ 1 \cdot 7 \cdot 1 \cdot 25\cdot 1 \cdot 3 \cdot 1 \cdot 1 ~\backslash~ 9
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\\
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10 ~/~ 1 \cdot 1 \cdot 1 \cdot 36\cdot 1 \cdot 2 \cdot 1 \cdot 8 \cdot 1 ~\backslash~ 10
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\end{matrix}</math>
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|}
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===ASCII===
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<pre>
 +
Example
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    *                      n o m
 +
    *                      \ /
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    *                      1 . 1
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    *                    \ / \ /
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    *                    2 . 1 . 2
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    *                  \ / \ / \ /
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    *                  3 . 1 . 1 . 3
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    *                \ / \ / \ / \ /
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    *                4 . 1 . 2 . 1 . 4
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    *              \ / \ / \ / \ / \ /
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    *              5 . 1 . 3 . 1 . 1 . 5
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    *            \ / \ / \ / \ / \ / \ /
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    *            6 . 1 . 1 . 1 . 4 . 1 . 6
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    *          \ / \ / \ / \ / \ / \ / \ /
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    *          7 . 1 . 5 . 2 . 9 . 1 . 1 . 7
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    *        \ / \ / \ / \ / \ / \ / \ / \ /
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    *        8 . 1 . 6 . 1 . 1 . 1 . 2 . 1 . 8
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    *      \ / \ / \ / \ / \ / \ / \ / \ / \ /
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    *      9 . 1 . 7 . 1 . 25. 1 . 3 . 1 . 1 . 9
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    *    \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
 +
    *  10 . 1 . 1 . 1 . 36. 1 . 2 . 1 . 8 . 1 . 10
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    *
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    * Primal codes of finite partial functions on positive integers:
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    * 1 = { }
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    * 2 = 1:1
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    * 3 = 2:1
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    * 4 = 1:2
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    * 5 = 3:1
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    * 6 = 1:1 2:1
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    * 7 = 4:1
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    * 8 = 1:3
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    * 9 = 2:2
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    * 10 = 1:1 3:1
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    * 11 = 5:1
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    * 12 = 1:2 2:1
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    * 13 = 6:1
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    * 14 = 1:1 4:1
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    * 15 = 2:1 3:1
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    * 16 = 1:4
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    * 17 = 7:1
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    * 18 = 1:1 2:2
 +
    * 19 = 8:1
 +
    * 20 = 1:2 3:1
 +
</pre>
    
==A109300==
 
==A109300==
Jon Awbrey
12,136

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