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Euler has design of a homepage and there is a link back to the overview for each solution.

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Felix Martin
2018-06-14 20:11:26 -04:00
parent 894160d1a0
commit c34ebd6181
48 changed files with 1134 additions and 2394 deletions
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ipython/html/EulerProblem029.html
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<title>EulerProblem029</title><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
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<h1 id="Euler-Problem-29">Euler Problem 29<a class="anchor-link" href="#Euler-Problem-29">&#182;</a></h1><p>Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:</p>
<h1 id="Euler-Problem-29">Euler Problem 29<a class="anchor-link" href="#Euler-Problem-29"></a></h1><p><a href="/euler">Back to overview.</a></p><p>Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:</p>
<p>$2^2=4, 2^3=8, 2^4=16, 2^5=32$</p>
<p>$3^2=9, 3^3=27, 3^4=81, 3^5=243$</p>
<p>$4^2=16, 4^3=64, 4^4=256, 4^5=1024$</p>
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<p>If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:</p>
<p>$4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125$</p>
<p>How many distinct terms are in the sequence generated by $a^b$ for $2 ≤ a ≤ 100$ and $2 ≤ b ≤ 100$?</p>
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<div class="prompt input_prompt">In&nbsp;[1]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">s</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="n">a</span><span class="o">**</span><span class="n">b</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">101</span><span class="p">)</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">101</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">9183</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
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<pre>9183
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