Hellus, Michael and Rechenauer, Anton and Waldi, Rolf (2020) Numerical semigroups generated by primes. SEMIGROUP FORUM, 101 (3). pp. 690-703. ISSN 0037-1912, 1432-2137
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Let p(1) = 2, p(2) = 3, p(3) = 5,. be the consecutive prime numbers, S-n the numerical semigroup generated by the primes not less than p(n) and u(n) the largest irredundant generator of S-n. We will show, that u(n) similar to 3p(n). Similarly, for the largest integer f(n) not contained in S-n, by computational evidence (https://www.uni-regensburg.de/Fakul taeten/nat_Fak_I/Hellus/table 1.pdf) we suspect that (1) f(n) is an odd number for n = 5 and (2) f(n) similar to 3p n; further (3) 4p(n) > f(n+1) for n >= 1. If f n is odd for large n, then f(n) similar to 3p(n). In case f(n) similar to 3p(n) every large even integer x is the sum of two primes. If 4p(n) > f(n+1) for n >= 1, then the Goldbach conjecture holds true. Further, Wilf's question in Wilf (Am Math Mon 85:562-565, 1978) has a positive answer for the semigroups S-n.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Numerical semigroup; Diophantine Frobenius problem; Goldbach conjecture; Wilf's conjecture on numerical semigroups |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Michael Hellus Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Rolf Waldi Mathematics > Professoren und akademische Räte im Ruhestand |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Mar 2021 09:31 |
| Last Modified: | 23 Mar 2021 09:31 |
| URI: | https://pred.uni-regensburg.de/id/eprint/44517 |
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