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Additive Properties of the Evil and Odious Numbers and Similar Sequences
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
-
Abstract
- First we reprove two results in additive number theory due to Dombi and Chen & Wang, respectively, on the number of representations of n as the sum of two odious or evil numbers, using techniques from automata theory and logic. We also use this technique to prove a new result about the numbers represented by five summands. Furthermore, we prove some new results on the tenfold sums of the evil and odious numbers, as well as k-fold sums of similar sequences of integers, by using techniques of analytic number theory involving trigonometric sums associated with the (+-1)-characteristic sequences of these integers.<br />Revision of previous version, with new author and results added
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....0d4f09853cca5c76e942d792c4920be2
- Full Text :
- https://doi.org/10.48550/arxiv.2112.13627