1. On Romanoff's constant
- Author
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Chen, Yong-Gao and Sun, Xue-Gong
- Subjects
- *
NATURAL numbers , *RATIONAL numbers , *REAL numbers , *INTEGERS , *MATHEMATICS - Abstract
In 1934, Romanoff proved that there are a positive proportion natural numbers which can be expressed as the sum of a prime and a power of 2. In this paper, a quantitative version of this theorem is given. We show that the proportion is larger than 0.0868 and for a positive proportion of odd integers the number of such representations is between 1 and 16. [Copyright &y& Elsevier]
- Published
- 2004
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