User:Jon Awbrey/Figures and Tables 22

Riffs and Rotes

59281

• Persiflage • 59281

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DRF 59281

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${\begin{array}{l}59281~{\text{is the}}~5995^{\text{th}}~{\text{prime}}\\\mathrm {pi} (59281)=5995\end{array}}$

${\begin{array}{rcl}59281&=&p_{5995}\\5995&=&5\cdot 11\cdot 109\\5995&=&p_{3}p_{5}p_{29}\\29&=&p_{10}\\10&=&p_{1}p_{3}\\[8pt]59281&=&p_{5995}\\&=&p_{p_{3}p_{5}p_{29}}\\&=&p_{p_{p_{2}}p_{p_{3}}p_{p_{10}}}\\&=&p_{p_{p_{p_{1}}}p_{p_{p_{2}}}p_{p_{p_{1}p_{3}}}}\\&=&p_{p_{p_{p_{1}}}p_{p_{p_{p_{1}}}}p_{p_{p_{1}p_{p_{2}}}}}\\&=&p_{p_{p_{p_{1}}}p_{p_{p_{p_{1}}}}p_{p_{p_{1}p_{p_{p_{1}}}}}}\\&=&p_{p_{p_{p}}p_{p_{p_{p}}}p_{p_{pp_{p_{p}}}}}\\[8pt]59281&=&p_{5995}\\&=&p_{p_{p_{p}}p_{p_{p_{p}}}p_{p_{pp_{p_{p}}}}}\end{array}}$

PNG

Riff 59281

Rote 59281

Squarefree All The Way Down (SATWD)

Riffs in Numerical Order

${\text{Riffs in Numerical Order}}\!$

$1\!$ ${\begin{array}{l}\varnothing \\1\end{array}}$	${\text{p}}\!$ ${\begin{array}{l}1\!:\!1\\2\end{array}}$	${\text{p}}_{\text{p}}\!$ ${\begin{array}{l}2\!:\!1\\3\end{array}}$	${\text{p}}^{\text{p}}\!$ ${\begin{array}{l}1\!:\!2\\4\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}3\!:\!1\\5\end{array}}$
${\text{p}}{\text{p}}_{\text{p}}\!$ ${\begin{array}{l}1\!:\!1~~2\!:\!1\\6\end{array}}$	${\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}4\!:\!1\\7\end{array}}$	${\text{p}}^{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!3\\8\end{array}}$	${\text{p}}_{\text{p}}^{\text{p}}\!$ ${\begin{array}{l}2\!:\!2\\9\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~3\!:\!1\\10\end{array}}$
${\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}5\!:\!1\\11\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{\text{p}}\!$ ${\begin{array}{l}1\!:\!2~~2\!:\!1\\12\end{array}}$	${\text{p}}_{{\text{p}}{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}6\!:\!1\\13\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~4\!:\!1\\14\end{array}}$	${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}2\!:\!1~~3\!:\!1\\15\end{array}}$
${\text{p}}^{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!4\\16\end{array}}$	${\text{p}}_{{\text{p}}_{{\text{p}}^{\text{p}}}}\!$ ${\begin{array}{l}7\!:\!1\\17\end{array}}$	${\text{p}}{\text{p}}_{\text{p}}^{\text{p}}\!$ ${\begin{array}{l}1\!:\!1~~2\!:\!2\\18\end{array}}$	${\text{p}}_{{\text{p}}^{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}8\!:\!1\\19\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!2~~3\!:\!1\\20\end{array}}$
${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}2\!:\!1~~4\!:\!1\\21\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!1~~5\!:\!1\\22\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}9\!:\!1\\23\end{array}}$	${\text{p}}^{{\text{p}}_{\text{p}}}{\text{p}}_{\text{p}}\!$ ${\begin{array}{l}1\!:\!3~~2\!:\!1\\24\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}}^{\text{p}}\!$ ${\begin{array}{l}3\!:\!2\\25\end{array}}$
${\text{p}}{\text{p}}_{{\text{p}}{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~6\!:\!1\\26\end{array}}$	${\text{p}}_{\text{p}}^{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}2\!:\!3\\27\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!2~~4\!:\!1\\28\end{array}}$	${\text{p}}_{{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}10\!:\!1\\29\end{array}}$	${\text{p}}{\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~2\!:\!1~~3\!:\!1\\30\end{array}}$
${\text{p}}_{{\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}}\!$ ${\begin{array}{l}11\!:\!1\\31\end{array}}$	${\text{p}}^{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!5\\32\end{array}}$	${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}2\!:\!1~~5\!:\!1\\33\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}_{{\text{p}}^{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!1~~7\!:\!1\\34\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}3\!:\!1~~4\!:\!1\\35\end{array}}$
${\text{p}}^{\text{p}}{\text{p}}_{\text{p}}^{\text{p}}\!$ ${\begin{array}{l}1\!:\!2~~2\!:\!2\\36\end{array}}$	${\text{p}}_{{\text{p}}^{\text{p}}{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}12\!:\!1\\37\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}^{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!1~~8\!:\!1\\38\end{array}}$	${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}2\!:\!1~~6\!:\!1\\39\end{array}}$	${\text{p}}^{{\text{p}}_{\text{p}}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!3~~3\!:\!1\\40\end{array}}$
${\text{p}}_{{\text{p}}_{{\text{p}}{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}13\!:\!1\\41\end{array}}$	${\text{p}}{\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~2\!:\!1~~4\!:\!1\\42\end{array}}$	${\text{p}}_{{\text{p}}{\text{p}}_{{\text{p}}^{\text{p}}}}\!$ ${\begin{array}{l}14\!:\!1\\43\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!2~~5\!:\!1\\44\end{array}}$	${\text{p}}_{\text{p}}^{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}2\!:\!2~~3\!:\!1\\45\end{array}}$
${\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~9\!:\!1\\46\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}15\!:\!1\\47\end{array}}$	${\text{p}}^{{\text{p}}^{\text{p}}}{\text{p}}_{\text{p}}\!$ ${\begin{array}{l}1\!:\!4~~2\!:\!1\\48\end{array}}$	${\text{p}}_{{\text{p}}^{\text{p}}}^{\text{p}}\!$ ${\begin{array}{l}4\!:\!2\\49\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}^{\text{p}}\!$ ${\begin{array}{l}1\!:\!1~~3\!:\!2\\50\end{array}}$
${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{{\text{p}}^{\text{p}}}}\!$ ${\begin{array}{l}2\!:\!1~~7\!:\!1\\51\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{{\text{p}}{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!2~~6\!:\!1\\52\end{array}}$	${\text{p}}_{{\text{p}}^{{\text{p}}^{\text{p}}}}\!$ ${\begin{array}{l}16\!:\!1\\53\end{array}}$	${\text{p}}{\text{p}}_{\text{p}}^{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~2\!:\!3\\54\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}}{\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}3\!:\!1~~5\!:\!1\\55\end{array}}$
${\text{p}}^{{\text{p}}_{\text{p}}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!3~~4\!:\!1\\56\end{array}}$	${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}^{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}2\!:\!1~~8\!:\!1\\57\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!1~~10\!:\!1\\58\end{array}}$	${\text{p}}_{{\text{p}}_{{\text{p}}_{{\text{p}}^{\text{p}}}}}\!$ ${\begin{array}{l}17\!:\!1\\59\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!2~~2\!:\!1~~3\!:\!1\\60\end{array}}$

Rotes in Numerical Order

${\text{Rotes in Numerical Order}}\!$

$1\!$ ${\begin{array}{l}\varnothing \\1\end{array}}$	${\text{p}}\!$ ${\begin{array}{l}1\!:\!1\\2\end{array}}$	${\text{p}}_{\text{p}}\!$ ${\begin{array}{l}2\!:\!1\\3\end{array}}$	${\text{p}}^{\text{p}}\!$ ${\begin{array}{l}1\!:\!2\\4\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}3\!:\!1\\5\end{array}}$
${\text{p}}{\text{p}}_{\text{p}}\!$ ${\begin{array}{l}1\!:\!1~~2\!:\!1\\6\end{array}}$	${\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}4\!:\!1\\7\end{array}}$	${\text{p}}^{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!3\\8\end{array}}$	${\text{p}}_{\text{p}}^{\text{p}}\!$ ${\begin{array}{l}2\!:\!2\\9\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~3\!:\!1\\10\end{array}}$
${\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}5\!:\!1\\11\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{\text{p}}\!$ ${\begin{array}{l}1\!:\!2~~2\!:\!1\\12\end{array}}$	${\text{p}}_{{\text{p}}{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}6\!:\!1\\13\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~4\!:\!1\\14\end{array}}$	${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}2\!:\!1~~3\!:\!1\\15\end{array}}$
${\text{p}}^{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!4\\16\end{array}}$	${\text{p}}_{{\text{p}}_{{\text{p}}^{\text{p}}}}\!$ ${\begin{array}{l}7\!:\!1\\17\end{array}}$	${\text{p}}{\text{p}}_{\text{p}}^{\text{p}}\!$ ${\begin{array}{l}1\!:\!1~~2\!:\!2\\18\end{array}}$	${\text{p}}_{{\text{p}}^{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}8\!:\!1\\19\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!2~~3\!:\!1\\20\end{array}}$
${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}2\!:\!1~~4\!:\!1\\21\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!1~~5\!:\!1\\22\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}9\!:\!1\\23\end{array}}$	${\text{p}}^{{\text{p}}_{\text{p}}}{\text{p}}_{\text{p}}\!$ ${\begin{array}{l}1\!:\!3~~2\!:\!1\\24\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}}^{\text{p}}\!$ ${\begin{array}{l}3\!:\!2\\25\end{array}}$
${\text{p}}{\text{p}}_{{\text{p}}{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~6\!:\!1\\26\end{array}}$	${\text{p}}_{\text{p}}^{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}2\!:\!3\\27\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!2~~4\!:\!1\\28\end{array}}$	${\text{p}}_{{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}10\!:\!1\\29\end{array}}$	${\text{p}}{\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~2\!:\!1~~3\!:\!1\\30\end{array}}$
${\text{p}}_{{\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}}\!$ ${\begin{array}{l}11\!:\!1\\31\end{array}}$	${\text{p}}^{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!5\\32\end{array}}$	${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}2\!:\!1~~5\!:\!1\\33\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}_{{\text{p}}^{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!1~~7\!:\!1\\34\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}3\!:\!1~~4\!:\!1\\35\end{array}}$
${\text{p}}^{\text{p}}{\text{p}}_{\text{p}}^{\text{p}}\!$ ${\begin{array}{l}1\!:\!2~~2\!:\!2\\36\end{array}}$	${\text{p}}_{{\text{p}}^{\text{p}}{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}12\!:\!1\\37\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}^{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!1~~8\!:\!1\\38\end{array}}$	${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}2\!:\!1~~6\!:\!1\\39\end{array}}$	${\text{p}}^{{\text{p}}_{\text{p}}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!3~~3\!:\!1\\40\end{array}}$
${\text{p}}_{{\text{p}}_{{\text{p}}{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}13\!:\!1\\41\end{array}}$	${\text{p}}{\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~2\!:\!1~~4\!:\!1\\42\end{array}}$	${\text{p}}_{{\text{p}}{\text{p}}_{{\text{p}}^{\text{p}}}}\!$ ${\begin{array}{l}14\!:\!1\\43\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!2~~5\!:\!1\\44\end{array}}$	${\text{p}}_{\text{p}}^{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}2\!:\!2~~3\!:\!1\\45\end{array}}$
${\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~9\!:\!1\\46\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}15\!:\!1\\47\end{array}}$	${\text{p}}^{{\text{p}}^{\text{p}}}{\text{p}}_{\text{p}}\!$ ${\begin{array}{l}1\!:\!4~~2\!:\!1\\48\end{array}}$	${\text{p}}_{{\text{p}}^{\text{p}}}^{\text{p}}\!$ ${\begin{array}{l}4\!:\!2\\49\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}^{\text{p}}\!$ ${\begin{array}{l}1\!:\!1~~3\!:\!2\\50\end{array}}$
${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{{\text{p}}^{\text{p}}}}\!$ ${\begin{array}{l}2\!:\!1~~7\!:\!1\\51\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{{\text{p}}{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!2~~6\!:\!1\\52\end{array}}$	${\text{p}}_{{\text{p}}^{{\text{p}}^{\text{p}}}}\!$ ${\begin{array}{l}16\!:\!1\\53\end{array}}$	${\text{p}}{\text{p}}_{\text{p}}^{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!1~~2\!:\!3\\54\end{array}}$	${\text{p}}_{{\text{p}}_{\text{p}}}{\text{p}}_{{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}3\!:\!1~~5\!:\!1\\55\end{array}}$
${\text{p}}^{{\text{p}}_{\text{p}}}{\text{p}}_{{\text{p}}^{\text{p}}}\!$ ${\begin{array}{l}1\!:\!3~~4\!:\!1\\56\end{array}}$	${\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}^{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}2\!:\!1~~8\!:\!1\\57\end{array}}$	${\text{p}}{\text{p}}_{{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}}\!$ ${\begin{array}{l}1\!:\!1~~10\!:\!1\\58\end{array}}$	${\text{p}}_{{\text{p}}_{{\text{p}}_{{\text{p}}^{\text{p}}}}}\!$ ${\begin{array}{l}17\!:\!1\\59\end{array}}$	${\text{p}}^{\text{p}}{\text{p}}_{\text{p}}{\text{p}}_{{\text{p}}_{\text{p}}}\!$ ${\begin{array}{l}1\!:\!2~~2\!:\!1~~3\!:\!1\\60\end{array}}$