Primitive substitutive numbers are closed under rational multiplication
Journal de théorie des nombres de Bordeaux, Tome 10 (1998) no. 2, pp. 315-320.

Soit M(r) l’ensemble des réels α dont le développement en base r contient une queue qui est l’image d’un point fixe d’une substitution primitive par un morphisme de lettres. Nous démontrons que l’ensemble M(r) est stable par multiplication par les rationnels, mais non stable par addition.

Let M(r) denote the set of real numbers α whose base-r digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution. We show that the set M(r) is closed under multiplication by rational numbers, but not closed under addition.

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     author = {Pallavi Ketkar and Luca Q. Zamboni},
     title = {Primitive substitutive numbers are closed under rational multiplication},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {315--320},
     publisher = {Universit\'e Bordeaux I},
     volume = {10},
     number = {2},
     year = {1998},
     zbl = {0930.11008},
     mrnumber = {1828248},
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Pallavi Ketkar; Luca Q. Zamboni. Primitive substitutive numbers are closed under rational multiplication. Journal de théorie des nombres de Bordeaux, Tome 10 (1998) no. 2, pp. 315-320. https://jtnb.centre-mersenne.org/item/JTNB_1998__10_2_315_0/

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