List of superparticular intervals: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-08-13 13:43:18 UTC</tt>.

: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-08-13 18:10:05 UTC</tt>.

: The original revision id was <tt>~~616359767~~</tt>.

: The original revision id was <tt>616363773</tt>.

: The revision comment was: <tt>~~added OEIS link~~</tt>

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<h4>Original Wikitext content:</h4>

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The list below is ordered by [[harmonic limit]], or the largest prime involved in the prime factorization. [[36_35|36/35]], for instance, is an interval of the [[7-limit]], as it factors to (22*32)/(5*7), while 37/36 would belong to the 37-limit.

[[http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem|Størmer's theorem]] guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. [[~~https~~://oeis.org/A145604|~~OEIS~~ A145604]] gives the number of superparticular ratios in each prime limit.

[[http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem|Størmer's theorem]] guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. OEIS [[http://oeis.org/A145604|A145604]] gives the number of superparticular ratios in each prime limit, and [[http://oeis.org/A117581|A117581]] the largest numerator for each prime limit.

See also: [[Gallery of Just Intervals]]. Many of the names below come from [[http://www.huygens-fokker.org/docs/intervals.html|here]].

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The list below is ordered by <a class="wiki_link" href="/harmonic%20limit">harmonic limit</a>, or the largest prime involved in the prime factorization. <a class="wiki_link" href="/36_35">36/35</a>, for instance, is an interval of the <a class="wiki_link" href="/7-limit">7-limit</a>, as it factors to (22*32)/(5*7), while 37/36 would belong to the 37-limit.

<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem" rel="nofollow">Størmer's theorem</a> guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. <a class="wiki_link_ext" href="~~https~~://oeis.org/A145604" rel="nofollow">~~OEIS~~ A145604</a> gives the number of superparticular ratios in each prime limit.

<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem" rel="nofollow">Størmer's theorem</a> guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. OEIS <a class="wiki_link_ext" href="http://oeis.org/A145604" rel="nofollow">A145604</a> gives the number of superparticular ratios in each prime limit, and <a class="wiki_link_ext" href="http://oeis.org/A117581" rel="nofollow">A117581</a> the largest numerator for each prime limit.

See also: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a>. Many of the names below come from <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow">here</a>.

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-08-13 13:43:18 UTC</tt>.<br>
+: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-08-13 18:10:05 UTC</tt>.<br>
-: The original revision id was <tt>616359767</tt>.<br>
+: The original revision id was <tt>616363773</tt>.<br>
-: The revision comment was: <tt>added OEIS link</tt><br>
+: The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 10: / Line 10: @@
 The list below is ordered by [[harmonic limit]], or the largest prime involved in the prime factorization. [[36_35|36/35]], for instance, is an interval of the [[7-limit]], as it factors to (2&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;)/(5*7), while 37/36 would belong to the 37-limit.
-[[http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem|Størmer's theorem]] guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. [[https://oeis.org/A145604|OEIS A145604]] gives the number of superparticular ratios in each prime limit.
+[[http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem|Størmer's theorem]] guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. OEIS [[http://oeis.org/A145604|A145604]] gives the number of superparticular ratios in each prime limit, and [[http://oeis.org/A117581|A117581]] the largest numerator for each prime limit.
 See also: [[Gallery of Just Intervals]]. Many of the names below come from [[http://www.huygens-fokker.org/docs/intervals.html|here]].
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 The list below is ordered by &lt;a class="wiki_link" href="/harmonic%20limit"&gt;harmonic limit&lt;/a&gt;, or the largest prime involved in the prime factorization. &lt;a class="wiki_link" href="/36_35"&gt;36/35&lt;/a&gt;, for instance, is an interval of the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, as it factors to (2&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="font-size: 70%; vertical-align: super;"&gt;2&lt;/span&gt;)/(5*7), while 37/36 would belong to the 37-limit.&lt;br /&gt;
 &lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem" rel="nofollow"&gt;Størmer's theorem&lt;/a&gt; guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. &lt;a class="wiki_link_ext" href="https://oeis.org/A145604" rel="nofollow"&gt;OEIS A145604&lt;/a&gt; gives the number of superparticular ratios in each prime limit.&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem" rel="nofollow"&gt;Størmer's theorem&lt;/a&gt; guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. OEIS &lt;a class="wiki_link_ext" href="http://oeis.org/A145604" rel="nofollow"&gt;A145604&lt;/a&gt; gives the number of superparticular ratios in each prime limit, and &lt;a class="wiki_link_ext" href="http://oeis.org/A117581" rel="nofollow"&gt;A117581&lt;/a&gt; the largest numerator for each prime limit.&lt;br /&gt;
 &lt;br /&gt;
 See also: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;. Many of the names below come from &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow"&gt;here&lt;/a&gt;.&lt;br /&gt;