EXPANSIONS OF REAL NUMBERS IN NON-INTEGER BASES

Title & Authors
EXPANSIONS OF REAL NUMBERS IN NON-INTEGER BASES
Chunarom, Danita; Laohakosol, Vichian;

Abstract
The works of Erd$\small{\ddot{o}}$s et al. about expansions of 1 with respect to a non-integer base q, referred to as q-expansions, are investigated to determine how far they continue to hold when the number 1 is replaced by a positive number x. It is found that most results about q-expansions for real numbers greater than or equal to 1 are in somewhat opposite direction to those for real numbers less than or equal to 1. The situation when a real number has a unique q-expansion, and when it has exactly two q-expansions are studied. The smallest base number q yielding a unique q-expansion is determined and a particular sequence is shown, in certain sense, to be the smallest sequence whose corresponding base number q yields exactly two q-expansions.
Keywords
expansions of numbers;non-integer bases;
Language
English
Cited by
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