Abstract
The restricted order of an asymptotic basis A is the least integer h, if it exists, such that every sufficiently large integer is the sum of h or fewer distinct elements of A. We show that any asymptotic basis of order 2 has a restricted order at most equal to 4. We also provide an example of an additive basis of order 2 whose restricted order is 4.
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References
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To Jean-Louis Nicolas
2000 Mathematics Subject Classification: Primary—11B13
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Hennecart, F. On the Restricted Order of Asymptotic Bases of Order Two. Ramanujan J 9, 123–130 (2005). https://doi.org/10.1007/s11139-005-0830-8
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DOI: https://doi.org/10.1007/s11139-005-0830-8