{"status": "success", "data": {"description_md": "**POTD May 29, 2024**\n\nFor positive integers $x$, let $g(x)$ be the number of blocks of consecutive 1\u2019s in the binary expansion of $x$. For example, $g(19) = 2$ because $19 = 10011_2$ has a block of one $1$ at the beginning and a block of two 1\u2019s at the end, and $g(7) = 1$ because $7 = 111_2$ only has a single block of three $1$\u2019s. Compute $g(1) + g(2) + g(3) + \\cdots + g(256).$", "description_html": "<p><strong>POTD May 29, 2024</strong></p>&#10;<p>For positive integers <span class=\"katex--inline\">x</span>, let <span class=\"katex--inline\">g(x)</span> be the number of blocks of consecutive 1&#8217;s in the binary expansion of <span class=\"katex--inline\">x</span>. For example, <span class=\"katex--inline\">g(19) = 2</span> because <span class=\"katex--inline\">19 = 10011_2</span> has a block of one <span class=\"katex--inline\">1</span> at the beginning and a block of two 1&#8217;s at the end, and <span class=\"katex--inline\">g(7) = 1</span> because <span class=\"katex--inline\">7 = 111_2</span> only has a single block of three <span class=\"katex--inline\">1</span>&#8217;s. Compute <span class=\"katex--inline\">g(1) + g(2) + g(3) + \\cdots + g(256).</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #171", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}