Komornik–Loreti constant
In the mathematical theory of non-standard positional numeral systems, the Komornik–Loreti constant is a mathematical constant that represents the smallest base "q" for which the number 1 has a unique representation, called its "q"-development. The constant is named after Vilmos Komornik and Paola Loreti, who defined it in 1998. Definition. Given a real number "q" > 1, the series is called the "q"-expansion, or formula_2-expansion, of the positive real number "x" if, for all formula_3, formula_4, where formula_5 is the floor function and formula_6 need not be an integer. Any real number formula_7 such  that formula_8 has such an expansion, as can be found using the greedy algorithm. The special case of formula_9, formula_10, and formula_11 or 1 is sometimes called a formula_12-development. formula_13 gives the only 2-development. However, for almost all formula_14, there are an infinite number of different formula_12-developments. Even more surprisingly though, there exist exceptional formula_16 for which there exists only a single formula_12-development. Furthermore, there is a smallest number formula_14 known as the Komornik–Loreti constant for which there exists a unique formula_12-development. Value. The Komornik–Loreti constant is the value formula_12 such that where  formula_22 is the Thue–Morse sequence, i.e., formula_22 is the parity of the number of 1's in the binary representation of formula_24. It has approximate value The constant formula_12 is also the unique positive real root of This constant is transcendental.