statement.html

problem 14 · 11 lines

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<p>The following iterative sequence is defined for the set of positive integers:</p>
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<li>$n \to n/2$ ($n$ is even)</li>
<li>$n \to 3n + 1$ ($n$ is odd)</li></ul>
<p>Using the rule above and starting with $13$, we generate the following sequence:
$$13 \to 40 \to 20 \to 10 \to 5 \to 16 \to 8 \to 4 \to 2 \to 1.$$</p>
<p>It can be seen that this sequence (starting at $13$ and finishing at $1$) contains $10$ terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at $1$.</p>
<p>Which starting number, under one million, produces the longest chain?</p>
<p class="note"><b>NOTE:</b> Once the chain starts the terms are allowed to go above one million.</p>
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