Vulcan Constant

Concantenate the set of all Bit Strings of increasing length in numerical order $\{ 0, 1, 00, 01, 10, 11, ... \}$ and interpret as a binary fraction $\mathbb{V_c} := .0100011011...$.

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The decimal expansion of the Vulcan Constant is $\mathbb{V_{c_{10}}} := 0.276387117279486523734198676211901230555089988160685506143676819115...$.