{"status": "success", "data": {"description_md": "Let $a_1$, $a_2$, $a_3$, $\\ldots$, $a_n$  be a sequence satisfying the following properties:\n- $a_1 = 1$\n- For each positive integer $n>1$, $a_n$ is the smallest positive integer such that there do not exist (not necessarily distinct) positive integers $i,j < n$ with $a_i-a_j=a_j-a_n$.\n\nFind the sum of the first $24$ terms in this sequence.", "description_html": "<p>Let <span class=\"katex--inline\">a_1</span>, <span class=\"katex--inline\">a_2</span>, <span class=\"katex--inline\">a_3</span>, <span class=\"katex--inline\">\\ldots</span>, <span class=\"katex--inline\">a_n</span>  be a sequence satisfying the following properties:</p>&#10;<ul>&#10;<li><span class=\"katex--inline\">a_1 = 1</span></li>&#10;<li>For each positive integer <span class=\"katex--inline\">n&gt;1</span>, <span class=\"katex--inline\">a_n</span> is the smallest positive integer such that there do not exist (not necessarily distinct) positive integers <span class=\"katex--inline\">i,j &lt; n</span> with <span class=\"katex--inline\">a_i-a_j=a_j-a_n</span>.</li>&#10;</ul>&#10;<p>Find the sum of the first <span class=\"katex--inline\">24</span> terms in this sequence.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 8, "problem_name": "TxO Math Bowl 2024 - Team Contest - Problem 29", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024team-p30", "prev": "/problem/txo2024team-p28"}}