{"status": "success", "data": {"description_md": "Let $S$ be the set of all positive integers $n$ such that there exists a nonnegative integer $k<n-1$ such that the numbers $\\binom{n}{k}$, $\\binom{n}{k+1}$, and $\\binom{n}{k+2}$ form an arithmetic sequence. Find the sum of the $10$ smallest elements in $S$.", "description_html": "<p>Let <span class=\"katex--inline\">S</span> be the set of all positive integers <span class=\"katex--inline\">n</span> such that there exists a nonnegative integer <span class=\"katex--inline\">k&lt;n-1</span> such that the numbers <span class=\"katex--inline\">\\binom{n}{k}</span>, <span class=\"katex--inline\">\\binom{n}{k+1}</span>, and <span class=\"katex--inline\">\\binom{n}{k+2}</span> form an arithmetic sequence. Find the sum of the <span class=\"katex--inline\">10</span> smallest elements in <span class=\"katex--inline\">S</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Christmas Contest - Team Round - Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_team-p20", "prev": "/problem/christmas1_team-p18"}}