Problem 68E

68. Find the first 40 terms of the sequence defined by

$$a_{n+1}=\left\{\begin{array}{ll}\frac{1}{2} a_{n} & \text { if } a_{n} \text { is an even number } \\3 a_{n}+1 & \text { if } a_{n} \text { is an odd number }\end{array}\right.$$

and $a_{1}=11 .$ Do the same if $a_{1}=25 .$ Make a conjecture about this type of sequence.

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