Finite and Infinite Arithmetic Progressions Related to Beta-Expansion
Let 1<β<2 and ε(x,β) be the β-expansion of x∈[0,1). Denote by Aβ(x) the set of positions where the digit 1 appears in ε(x,β). We consider the sets of points x such that Aβ(x) contains arbitrarily long arithmetic progressions and includes infinite arithmetic progressions, respectively. Their si...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/678769 |