{"status": "success", "data": {"description_md": "Let $a_1,a_2,\\ldots$ be a sequence determined by the rule $a_n=a_{n-1}/2$ if $a_{n-1}$ is even and $a_n=3a_{n-1}+1$ if $a_{n-1}$ is odd. For how many positive integers $a_1 \\le 2008$ is it true that $a_1$ is less than each of $a_2$, $a_3$, and $a_4$? \n\n$\\mathrm{(A)}\\ 250\\qquad\\mathrm{(B)}\\ 251\\qquad\\mathrm{(C)}\\ 501\\qquad\\mathrm{(D)}\\ 502\\qquad\\mathrm{(E)} 1004$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--inline\">a_1,a_2,\\ldots</span>  be a sequence determined by the rule  <span class=\"katex--inline\">a_n=a_{n-1}/2</span>  if  <span class=\"katex--inline\">a_{n-1}</span>  is even and  <span class=\"katex--inline\">a_n=3a_{n-1}+1</span>  if  <span class=\"katex--inline\">a_{n-1}</span>  is odd. For how many positive integers  <span class=\"katex--inline\">a_1 \\le 2008</span>  is it true that  <span class=\"katex--inline\">a_1</span>  is less than each of  <span class=\"katex--inline\">a_2</span> ,  <span class=\"katex--inline\">a_3</span> , and  <span class=\"katex--inline\">a_4</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 250\\qquad\\mathrm{(B)}\\ 251\\qquad\\mathrm{(C)}\\ 501\\qquad\\mathrm{(D)}\\ 502\\qquad\\mathrm{(E)} 1004</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2008 AMC 12A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12A_p18", "prev": "/problem/08_amc12A_p16"}}