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Felix Martin
2019-01-22 00:12:10 -05:00
parent 550a1479f0
commit b28b59fc7d
5 changed files with 12300 additions and 6 deletions
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<p>The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number, 134217728=89, is a ninth power.</p>
<p>The 5-digit number, 16807=$7^5$, is also a fifth power. Similarly, the 9-digit number, 134217728=$8^9$, is a ninth power.</p>
<p>How many n-digit positive integers exist which are also an nth power?</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">get_digit_count</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">&lt;</span> <span class="mi">10</span><span class="p">:</span>
<span class="k">return</span> <span class="mi">1</span>
<span class="n">c</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="n">n</span><span class="p">:</span>
<span class="n">n</span> <span class="o">//=</span> <span class="mi">10</span>
<span class="n">c</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">c</span>
<span class="k">assert</span><span class="p">(</span><span class="n">get_digit_count</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">assert</span><span class="p">(</span><span class="n">get_digit_count</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">assert</span><span class="p">(</span><span class="n">get_digit_count</span><span class="p">(</span><span class="mi">33</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span><span class="p">)</span>
<span class="k">assert</span><span class="p">(</span><span class="n">get_digit_count</span><span class="p">(</span><span class="mi">100</span><span class="p">)</span> <span class="o">==</span> <span class="mi">3</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">get_n_digit_positive_integers</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">r</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
<span class="k">if</span> <span class="n">get_digit_count</span><span class="p">(</span><span class="n">i</span> <span class="o">**</span> <span class="n">n</span><span class="p">)</span> <span class="o">==</span> <span class="n">n</span><span class="p">:</span>
<span class="n">r</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span> <span class="o">**</span> <span class="n">n</span><span class="p">)</span>
<span class="k">if</span> <span class="n">get_digit_count</span><span class="p">(</span><span class="n">i</span> <span class="o">**</span> <span class="n">n</span><span class="p">)</span> <span class="o">&gt;</span> <span class="n">n</span><span class="p">:</span>
<span class="k">return</span> <span class="n">r</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="nb">len</span><span class="p">(</span><span class="n">get_n_digit_positive_integers</span><span class="p">(</span><span class="n">n</span><span class="p">))</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)])</span>
<span class="nb">print</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="k">assert</span><span class="p">(</span><span class="n">s</span> <span class="o">==</span> <span class="mi">49</span><span class="p">)</span>
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<pre>49
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<td><a href="EulerProblem063.html">Problem 063</a></td>
<td></td>
<td>Sun, 6 Jan 2019, 06:17</td>
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<kbd>powers</kbd>
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<td><a href="EulerProblem064.html">Problem 064</a></td>
<td>Tue, 22 Jan 2019, 05:10</td>
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<kbd>fractions</kbd>
<kbd>square roots</kbd>
<kbd>sequence</kbd>
<kbd>periodic</kbd>
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