Minimal consistent EDOs: Difference between revisions
Wikispaces>genewardsmith **Imported revision 603235350 - Original comment: ** |
Wikispaces>TallKite **Imported revision 603954402 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-01-12 16:54:49 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>603954402</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">An [[edo]] N is | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">An [[edo]] N is [[consistent]] with respect to a set of rational numbers s if the [[patent val]] mapping of every element of s is the nearest N-edo approximation. It is //uniquely consistent// if every element of s is mapped to a unique value. If the set s is the q [[odd limit]], we say N is q-limit consistent and q-limit uniquely consistent, respectively. Below is a table of the least consistent, and least uniquely consistent, edo for every odd number up to 135. | ||
|| Odd limit || Smallest consistent || Smallest uniquely consistent || | || Odd limit || Smallest consistent || Smallest uniquely consistent || | ||
| Line 30: | Line 30: | ||
|| 39 || 311 || 2554 || | || 39 || 311 || 2554 || | ||
|| 41 || 311 || 2554 || | || 41 || 311 || 2554 || | ||
|| 43 ||17461 || 17461 || | || 43 || 17461 || 17461 || | ||
|| 45 || 17461 || 17461 || | || 45 || 17461 || 17461 || | ||
|| 47 || 20567 || 20567 || | || 47 || 20567 || 20567 || | ||
| Line 74: | Line 74: | ||
|| 129 || 2901533 || 2901533 || | || 129 || 2901533 || 2901533 || | ||
|| 131 || 2901533 || 2901533 || | || 131 || 2901533 || 2901533 || | ||
|| 133 || 70910024.|| 70910024.|| | || 133 || 70910024. || 70910024. || | ||
|| 135 || 70910024.|| 70910024.|| | || 135 || 70910024. || 70910024. || | ||
=OEIS integer sequences links= | =OEIS integer sequences links= | ||
[[http://oeis.org/A116474]] | [[http://oeis.org/A116474]] | ||
[[http://oeis.org/A116475]] | [[http://oeis.org/A116475]] | ||
| Line 83: | Line 83: | ||
[[http://oeis.org/A117578]]</pre></div> | [[http://oeis.org/A117578]]</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Minimal consistent EDOs</title></head><body>An <a class="wiki_link" href="/edo">edo</a> N is < | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Minimal consistent EDOs</title></head><body>An <a class="wiki_link" href="/edo">edo</a> N is <a class="wiki_link" href="/consistent">consistent</a> with respect to a set of rational numbers s if the <a class="wiki_link" href="/patent%20val">patent val</a> mapping of every element of s is the nearest N-edo approximation. It is <em>uniquely consistent</em> if every element of s is mapped to a unique value. If the set s is the q <a class="wiki_link" href="/odd%20limit">odd limit</a>, we say N is q-limit consistent and q-limit uniquely consistent, respectively. Below is a table of the least consistent, and least uniquely consistent, edo for every odd number up to 135.<br /> | ||
<br /> | <br /> | ||
| Line 636: | Line 636: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="OEIS integer sequences links"></a><!-- ws:end:WikiTextHeadingRule:0 -->OEIS integer sequences links</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="OEIS integer sequences links"></a><!-- ws:end:WikiTextHeadingRule:0 -->OEIS integer sequences links</h1> | ||
<a class="wiki_link_ext" href="http://oeis.org/A116474" rel="nofollow">http://oeis.org/A116474</a><br /> | <a class="wiki_link_ext" href="http://oeis.org/A116474" rel="nofollow">http://oeis.org/A116474</a><br /> | ||
<a class="wiki_link_ext" href="http://oeis.org/A116475" rel="nofollow">http://oeis.org/A116475</a><br /> | <a class="wiki_link_ext" href="http://oeis.org/A116475" rel="nofollow">http://oeis.org/A116475</a><br /> | ||
<a class="wiki_link_ext" href="http://oeis.org/A117577" rel="nofollow">http://oeis.org/A117577</a><br /> | <a class="wiki_link_ext" href="http://oeis.org/A117577" rel="nofollow">http://oeis.org/A117577</a><br /> | ||
<a class="wiki_link_ext" href="http://oeis.org/A117578" rel="nofollow">http://oeis.org/A117578</a></body></html></pre></div> | <a class="wiki_link_ext" href="http://oeis.org/A117578" rel="nofollow">http://oeis.org/A117578</a></body></html></pre></div> | ||