Primitive substitutive numbers are closed under rational multiplication
Pallavi Ketkar, Luca Quardo Zamboni · Journal de Théorie des Nombres de Bordeaux · 1998
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.