Minimal consistent EDOs: Difference between revisions

Revision as of 13:22, 7 January 2017

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author genewardsmith and made on 2017-01-07 13:22:37 UTC.

The original revision id was 603235350.

The revision comment was:

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

Original Wikitext content:

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 ||
|| 1 || 1 || 1 ||
|| 3 || 1 || 3 ||
|| 5 || 3 || 9 ||
|| 7 || 4 || 27 ||
|| 9 || 5 || 41 ||
|| 11 || 22 || 58 ||
|| 13 || 26 || 87 ||
|| 15 || 29 || 111 ||
|| 17 || 58 || 149 ||
|| 19 || 80 || 217 ||
|| 21 || 94 || 282 ||
|| 23 || 94 || 282 ||
|| 25 || 282 || 388 ||
|| 27 || 282 || 388 ||
|| 29 || 282 || 1323 ||
|| 31 || 311 || 1600 ||
|| 33 || 311 || 1600 ||
|| 35 || 311 || 1600 ||
|| 37 || 311 || 1600 ||
|| 39 || 311 || 2554 ||
|| 41 || 311 || 2554 ||
|| 43 ||17461 || 17461 ||
|| 45 || 17461 || 17461 ||
|| 47 || 20567 || 20567 ||
|| 49 || 20567 || 20567 ||
|| 51 || 20567 || 20567 ||
|| 53 || 20567 || 20567 ||
|| 55 || 20567 || 20567 ||
|| 57 || 20567 || 20567 ||
|| 59 || 253389 || 253389 ||
|| 61 || 625534 || 625534 ||
|| 63 || 625534 || 625534 ||
|| 65 || 625534 || 625534 ||
|| 67 || 625534 || 625534 ||
|| 69 || 759630 || 759630 ||
|| 71 || 759630 || 759630 ||
|| 73 || 759630 || 759630 ||
|| 75 || 2157429 || 2157429 ||
|| 77 || 2157429 || 2157429 ||
|| 79 || 2901533 || 2901533 ||
|| 81 || 2901533 || 2901533 ||
|| 83 || 2901533 || 2901533 ||
|| 85 || 2901533 || 2901533 ||
|| 87 || 2901533 || 2901533 ||
|| 91 || 2901533 || 2901533 ||
|| 93 || 2901533 || 2901533 ||
|| 95 || 2901533 || 2901533 ||
|| 97 || 2901533 || 2901533 ||
|| 99 || 2901533 || 2901533 ||
|| 101 || 2901533 || 2901533 ||
|| 103 || 2901533 || 2901533 ||
|| 105 || 2901533 || 2901533 ||
|| 107 || 2901533 || 2901533 ||
|| 109 || 2901533 || 2901533 ||
|| 111 || 2901533 || 2901533 ||
|| 113 || 2901533 || 2901533 ||
|| 115 || 2901533 || 2901533 ||
|| 117 || 2901533 || 2901533 ||
|| 119 || 2901533 || 2901533 ||
|| 121 || 2901533 || 2901533 ||
|| 123 || 2901533 || 2901533 ||
|| 125 || 2901533 || 2901533 ||
|| 127 || 2901533 || 2901533 ||
|| 129 || 2901533 || 2901533 ||
|| 131 || 2901533 || 2901533 ||
|| 133 || 70910024.|| 70910024.||
|| 135 || 70910024.|| 70910024.||

=OEIS integer sequences links=
[[http://oeis.org/A116474]]
[[http://oeis.org/A116475]]
[[http://oeis.org/A117577]]
[[http://oeis.org/A117578]]

Original HTML content:

<html><head><title>Minimal consistent EDOs</title></head><body>An <a class="wiki_link" href="/edo">edo</a> N is <em>consistent</em> 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 />


<table class="wiki_table">
    <tr>
        <td>Odd limit<br />
</td>
        <td>Smallest consistent<br />
</td>
        <td>Smallest uniquely consistent<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>3<br />
</td>
        <td>9<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>4<br />
</td>
        <td>27<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>5<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>22<br />
</td>
        <td>58<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>26<br />
</td>
        <td>87<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>29<br />
</td>
        <td>111<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>58<br />
</td>
        <td>149<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>80<br />
</td>
        <td>217<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>94<br />
</td>
        <td>282<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>94<br />
</td>
        <td>282<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>282<br />
</td>
        <td>388<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>282<br />
</td>
        <td>388<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>282<br />
</td>
        <td>1323<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>311<br />
</td>
        <td>1600<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>311<br />
</td>
        <td>1600<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>311<br />
</td>
        <td>1600<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>311<br />
</td>
        <td>1600<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>311<br />
</td>
        <td>2554<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>311<br />
</td>
        <td>2554<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>17461<br />
</td>
        <td>17461<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>17461<br />
</td>
        <td>17461<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>20567<br />
</td>
        <td>20567<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>20567<br />
</td>
        <td>20567<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>20567<br />
</td>
        <td>20567<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>20567<br />
</td>
        <td>20567<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>20567<br />
</td>
        <td>20567<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>20567<br />
</td>
        <td>20567<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>253389<br />
</td>
        <td>253389<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>625534<br />
</td>
        <td>625534<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>625534<br />
</td>
        <td>625534<br />
</td>
    </tr>
    <tr>
        <td>65<br />
</td>
        <td>625534<br />
</td>
        <td>625534<br />
</td>
    </tr>
    <tr>
        <td>67<br />
</td>
        <td>625534<br />
</td>
        <td>625534<br />
</td>
    </tr>
    <tr>
        <td>69<br />
</td>
        <td>759630<br />
</td>
        <td>759630<br />
</td>
    </tr>
    <tr>
        <td>71<br />
</td>
        <td>759630<br />
</td>
        <td>759630<br />
</td>
    </tr>
    <tr>
        <td>73<br />
</td>
        <td>759630<br />
</td>
        <td>759630<br />
</td>
    </tr>
    <tr>
        <td>75<br />
</td>
        <td>2157429<br />
</td>
        <td>2157429<br />
</td>
    </tr>
    <tr>
        <td>77<br />
</td>
        <td>2157429<br />
</td>
        <td>2157429<br />
</td>
    </tr>
    <tr>
        <td>79<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>81<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>83<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>85<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>87<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>91<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>93<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>95<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>97<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>99<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>101<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>103<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>105<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>107<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>109<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>111<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>113<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>115<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>117<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>119<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>121<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>123<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>125<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>127<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>129<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>131<br />
</td>
        <td>2901533<br />
</td>
        <td>2901533<br />
</td>
    </tr>
    <tr>
        <td>133<br />
</td>
        <td>70910024.<br />
</td>
        <td>70910024.<br />
</td>
    </tr>
    <tr>
        <td>135<br />
</td>
        <td>70910024.<br />
</td>
        <td>70910024.<br />
</td>
    </tr>
</table>

<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>
<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/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>

@@ Line 1: / Line 1: @@
 <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:genewardsmith|genewardsmith]] and made on <tt>2017-01-07 11:24:07 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2017-01-07 13:22:37 UTC</tt>.<br>
-: The original revision id was <tt>603231544</tt>.<br>
+: The original revision id was <tt>603235350</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>
@@ Line 77: / Line 77: @@
 || 135 || 70910024.|| 70910024.||
-**Links**
+=OEIS integer sequences links=
 [[http://oeis.org/A116474]]
 [[http://oeis.org/A116475]]
@@ Line 636: / Line 635: @@
 &lt;br /&gt;
-&lt;strong&gt;Links&lt;/strong&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="OEIS integer sequences links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;OEIS integer sequences links&lt;/h1&gt;
-&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://oeis.org/A116474" rel="nofollow"&gt;http://oeis.org/A116474&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://oeis.org/A116475" rel="nofollow"&gt;http://oeis.org/A116475&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://oeis.org/A117577" rel="nofollow"&gt;http://oeis.org/A117577&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://oeis.org/A117578" rel="nofollow"&gt;http://oeis.org/A117578&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Minimal consistent EDOs: Difference between revisions

Revision as of 13:22, 7 January 2017

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search