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1987 AMC 12 #29 - Recursive Sequence

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January 1, 2012
AMC

Problem Statement

Consider the sequence of numbers defined recursively by t1=1t_1=1 and for n>1n>1 by tn=1+t(n/2)t_n=1+t_{(n/2)} when nn is even and by tn=1t(n−1)t_n=\frac{1}{t_{(n-1)}} when nn is odd. Given that tn=1987t_n=\frac{19}{87}, the sum of the digits of nn is
<spanclass=′latex−bold′>(A)</span> 15<spanclass=′latex−bold′>(B)</span> 17<spanclass=′latex−bold′>(C)</span> 19<spanclass=′latex−bold′>(D)</span> 21<spanclass=′latex−bold′>(E)</span> 23 <span class='latex-bold'>(A)</span>\ 15 \qquad<span class='latex-bold'>(B)</span>\ 17 \qquad<span class='latex-bold'>(C)</span>\ 19 \qquad<span class='latex-bold'>(D)</span>\ 21 \qquad<span class='latex-bold'>(E)</span>\ 23
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