https://michaelnielsen.org/polymath/index.php?action=history&feed=atom&title=T32-invariant_sequences
T32-invariant sequences - Revision history
2026-04-07T23:41:30Z
Revision history for this page on the wiki
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https://michaelnielsen.org/polymath/index.php?title=T32-invariant_sequences&diff=2529&oldid=prev
Alec at 14:21, 10 January 2010
2010-01-10T14:21:16Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:21, 10 January 2010</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>A <math>T_k</math>-invariant sequence is one that satisfies <math>x_{kn} = x_n</math> for all <math>n</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>A <math>T_k</math>-invariant sequence is one that satisfies <math>x_{kn} = x_n</math> for all <math>n</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; 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;"><div>This sequence, of length <math>417</math>, is <math>T_{32}</math>-invariant:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; 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;"><div>This sequence, of length <math>417</math>, is <math>T_{32}</math>-invariant <ins style="font-weight: bold; text-decoration: none;">with discrepancy <math>2</math></ins>:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> 0 + + - - + + - + - - + - - - + + - + - - + + + - + - - + + + -</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> 0 + + - - + + - + - - + - - - + + - + - - + + + - + - - + + + -</div></td></tr>
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Alec
https://michaelnielsen.org/polymath/index.php?title=T32-invariant_sequences&diff=2525&oldid=prev
Alec: Sequence of length 417.
2010-01-10T14:02:07Z
<p>Sequence of length 417.</p>
<p><b>New page</b></p><div>A <math>T_k</math>-invariant sequence is one that satisfies <math>x_{kn} = x_n</math> for all <math>n</math>.<br />
<br />
This sequence, of length <math>417</math>, is <math>T_{32}</math>-invariant:<br />
<br />
0 + + - - + + - + - - + - - - + + - + - - + + + - + - - + + + -<br />
+ - - - + + - + - + - + - - + - - + + + + - - - - + + - + - - +<br />
+ + + - - - + + + - - - - + - + - + + - + + - - + + - - - + + +<br />
- + + - + - + - + - - - - + - + - + + - + + - + + - + - + - - +<br />
- - - + - + + + - - + - + + - + + - + - + - - + - - - + - + + +<br />
+ - + - - + - - + - + - + + - - - + + + - - + - + - - + - + + -<br />
+ + - + - + + - - - - + + + - - + - - + + + + - - - + - + - - +<br />
- + + - + + - + - + + - - - + + + - - - + + - - - + + + - + - -<br />
+ + + - - + - + - - + - + - + + - - - + + + - + + - - - + - + -<br />
- + - + - + + + + - - + - - + + + - - - + + + - - - + + - + + -<br />
- - - + + + - - + + - - - + + - + + + - + - - - - + - + + + - -<br />
+ + + - - - + - - + + + - + - - - + + + + - - + + - + - + - - +<br />
- - - + - + + + + - - - + + + - - + - + + - - - + - + + - + - +<br />
- +</div>
Alec