ON SMALL BASES FOR WHICH 1 HAS COUNTABLY MANY EXPANSIONS
Yuru Zou, Lijin Wang, Jian Lu, Simon Baker · Mathematika · 2016
Let . A -expansion of a number in is a sequence satisfying Let denote the set of for which there exists with a countable number of -expansions, and let denote the set of for which 1 has a countable number of -expansions. In Erdős et al [On the uniqueness of the expansions . Acta Math. Hungar. 58 (1991), 333–342] it was shown that , and in S. Baker [On small bases which admit countably many expansions. J. Number Theory 147 (2015), 515–532] it was shown that , where is the positive root of . In this paper we show that the second smallest point of is , the positive root of . En route to proving this result, we show that , where is the positive root of .