{"status": "success", "data": {"description_md": "For all positive integers $ x$, let<br>\n$$ f(x) = \\begin{cases}1 & \\text{if }x = 1 \\\\<br>\\frac x{10} & \\text{if }x\\text{ is divisible by 10} \\\\<br>x + 1 & \\text{otherwise}\\end{cases} $$and define a sequence as follows: $ x_1 = x$ and $ x_{n + 1} = f(x_n)$ for all positive integers $ n$. Let $ d(x)$ be the smallest $ n$ such that $ x_n = 1$. (For example, $ d(100) = 3$ and $ d(87) = 7$.) Let $ m$ be the number of positive integers $ x$ such that $ d(x) = 20$. Find the sum of the distinct prime factors of $ m$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>For all positive integers $ x<span class=\"katex--inline\">, let&lt;br&gt;</span>$ f(x) = \\begin{cases}1 &amp; \\text{if }x = 1 \\<br/>\\frac x{10} &amp; \\text{if }x\\text{ is divisible by 10} \\<br/>x + 1 &amp; \\text{otherwise}\\end{cases} $$and define a sequence as follows: $ x_1 = x$ and $ x_{n + 1} = f(x_n)$ for all positive integers $ n$. Let $ d(x)$ be the smallest $ n$ such that $ x_n = 1$. (For example, $ d(100) = 3$ and $ d(87) = 7$.) Let $ m$ be the number of positive integers $ x$ such that $ d(x) = 20$. Find the sum of the distinct prime factors of $ m$.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 6, "problem_name": "2004 AIME I Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/04_aime_I_p14"}}