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		<id>https://lem12.uksw.edu.pl/index.php?action=history&amp;feed=atom&amp;title=Plik%3ADrzewoHCpoModyfikacjach.png</id>
		<title>Plik:DrzewoHCpoModyfikacjach.png - Historia wersji</title>
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		<updated>2026-08-11T11:34:57Z</updated>
		<subtitle>Historia wersji tej strony wiki</subtitle>
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	<entry>
		<id>https://lem12.uksw.edu.pl/index.php?title=Plik:DrzewoHCpoModyfikacjach.png&amp;diff=3255&amp;oldid=prev</id>
		<title>AndrzejSalwicki o 16:17, 10 sie 2026</title>
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				<updated>2026-08-10T16:17:22Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← poprzednia wersja&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Wersja z 16:17, 10 sie 2026&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;=== This is the graph &amp;lt;math&amp;gt; HC &amp;lt;/math&amp;gt;&amp;#160; from another perspective===&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Yes! &amp;lt;br /&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# The odd numbers are permuted.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# All edges go to the left.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;=== Ordering the odd numbers&amp;#160; ===&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;=== Ordering the odd numbers&amp;#160; ===&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;We are ordering the odd numbers with respect to the length of &amp;lt;math&amp;gt; 3n+1 &amp;lt;/math&amp;gt; computations.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;We are ordering the odd numbers with respect to the length of &amp;lt;math&amp;gt; 3n+1 &amp;lt;/math&amp;gt; computations.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let &amp;lt;math&amp;gt; x &amp;lt;/math&amp;gt;be a number of multiplications by 3, let &amp;lt;math&amp;gt; z &amp;lt;/math&amp;gt; be the number of divisions by 2.We assume that the length of &amp;lt;math&amp;gt; 3n+1 &amp;lt;/math&amp;gt; computation is &amp;lt;math&amp;gt; x+z &amp;lt;/math&amp;gt;. &amp;lt;br /&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let &amp;lt;math&amp;gt; x &amp;lt;/math&amp;gt;be a number of multiplications by 3, let &amp;lt;math&amp;gt; z &amp;lt;/math&amp;gt; be the number of divisions by 2.We assume that the length of &amp;lt;math&amp;gt; 3n+1 &amp;lt;/math&amp;gt; computation is &amp;lt;math&amp;gt; x+z &amp;lt;/math&amp;gt;. &amp;lt;br /&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>AndrzejSalwicki</name></author>	</entry>

	<entry>
		<id>https://lem12.uksw.edu.pl/index.php?title=Plik:DrzewoHCpoModyfikacjach.png&amp;diff=3254&amp;oldid=prev</id>
		<title>AndrzejSalwicki o 14:50, 10 sie 2026</title>
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				<updated>2026-08-10T14:50:37Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← poprzednia wersja&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Wersja z 14:50, 10 sie 2026&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;=== Ordering the odd numbers&amp;#160; ===&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;We are ordering the odd numbers with respect to the length of &amp;lt;math&amp;gt; 3n+1 &amp;lt;/math&amp;gt; computations.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Let &amp;lt;math&amp;gt; x &amp;lt;/math&amp;gt;be a number of multiplications by 3, let &amp;lt;math&amp;gt; z &amp;lt;/math&amp;gt; be the number of divisions by 2.We assume that the length of &amp;lt;math&amp;gt; 3n+1 &amp;lt;/math&amp;gt; computation is &amp;lt;math&amp;gt; x+z &amp;lt;/math&amp;gt;. &amp;lt;br /&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>AndrzejSalwicki</name></author>	</entry>

	<entry>
		<id>https://lem12.uksw.edu.pl/index.php?title=Plik:DrzewoHCpoModyfikacjach.png&amp;diff=3230&amp;oldid=prev</id>
		<title>AndrzejSalwicki o 18:15, 8 sie 2026</title>
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				<updated>2026-08-08T18:15:38Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Nowa strona&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>AndrzejSalwicki</name></author>	</entry>

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