On the cardinality of β-expansions of some numbers
2016 ◽
Vol 12
(06)
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pp. 1497-1507
Keyword(s):
Let [Formula: see text]. It is well known that every [Formula: see text] has a [Formula: see text]-expansion of the form [Formula: see text] with [Formula: see text], where [Formula: see text] denotes the largest integer not exceeding [Formula: see text]. Let [Formula: see text] and [Formula: see text] denote the sets of all [Formula: see text]-expansions of [Formula: see text] and the set of [Formula: see text]-prefixes of all [Formula: see text]-expansions of [Formula: see text], respectively. We show that [Formula: see text], [Formula: see text] and [Formula: see text] are equivalent under a certain finiteness condition.
2008 ◽
Vol 24
(3)
◽
pp. 159-183
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Keyword(s):
1994 ◽
Vol 131
(2)
◽
pp. 271-294
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1983 ◽
Vol 35
(1)
◽
pp. 49-58
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1972 ◽
Vol 24
(6)
◽
pp. 1170-1177
◽
Keyword(s):
2015 ◽
Vol 182
(2)
◽
pp. 289-298
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