Hellus, Michael and Rechenauer, Anton and Waldi, Rolf (2021) On the Frobenius number of certain numerical semigroups. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 31 (03). pp. 519-532. ISSN 0218-1967, 1793-6500
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Let 0 < lambda <= 1, lambda is not an element of{2/4, 2/7, 2/10, 2/13, ... }, be a real and p a prime number, with [p,p + lambda p] containing at least two primes. Denote by f(lambda)(p) the largest integer which cannot be written as a sum of primes from [p,p + lambda p]. Then f(lambda)(p) similar to [2 + 2/lambda] p,as p goes to infinity. Further a question of Wilf about the "Money-Changing Problem" has a positive answer for all semigroups of multiplicity p containing the primes from [p, 2p]. In particular, this holds for the semigroup generated by all primes not less than p. The latter special case was already shown in a previous paper.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Numerical semigroups; diophantine Frobenius problem; Wilf's conjecture on numerical semigroups; Goldbach conjecture |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Michael Hellus Mathematics > Prof. Dr. Rolf Waldi |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 Jul 2022 04:49 |
| Last Modified: | 06 Jul 2022 04:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45616 |
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