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Directory:Jon Awbrey/Papers/Riffs and Rotes (view source)
Revision as of 15:40, 26 January 2010
, 15:40, 26 January 2010→A109301
* [http://oeis.org/wiki/A109301 OEIS Wiki Entry for A109301].
* [http://oeis.org/wiki/A109301 OEIS Wiki Entry for A109301].
; Example
: <p><math>802701 = 9 \cdot 89189 = \text{p}_2^2 \text{p}_{8638}^1</math></p>
: <p><math>\text{Writing}~ (\operatorname{prime}(i))^j ~\text{as}~ i\!:\!j, ~\text{we have:}</math></p>
: <p><math>\begin{array}{lllll}
802701
& = & 9 \cdot 89189
& = & 2\!:\!2 ~~ 8638\!:\!1
\\
8638
& = & 2 \cdot 7 \cdot 617
& = & 1\!:\!1 ~~ 4\!:\!1 ~~ 113\!:\!1
\\
113
& &
& = & 30\!:\!1
\\
30
& = & 2 \cdot 3 \cdot 5
& = & 1\!:\!1 ~~ 2\!:\!1 ~~ 3\!:\!1
\\
4
& &
& = & 1\!:\!2
\\
3
& &
& = & 2\!:\!1
\\
2
& &
& = & 1\!:\!1
\end{array}</math></p>
: <p><math>\text{As a result, the rote of 802701 is the graph:}</math></p>
:{| border="1" cellpadding="20"
| [[Image:Rote 802701 Big.jpg|330px]]
|}
: <p><math>\text{By inspection, the rote height of 802701 is 6.}</math></p>
<br>
{| align="center" border="1" cellpadding="6"
{| align="center" border="1" cellpadding="6"