On the Frobenius number of certain numerical semigroups

نویسندگان

چکیده

Let $0<\lambda\leq1$, $\lambda\notin\left\{\frac24, \frac27, \frac2{10}, \frac2{13}, \ldots\right\}$, be a real and $p$ prime number, with $[p,p+\lambda p]$ containing at least two primes. Denote by $f_\lambda(p)$ the largest integer which cannot written as sum of primes from p]$. Then \[f_\lambda(p)\sim\left\lfloor2+\frac2\lambda\right\rfloor\cdot p\text{, }p\text{ goes to infinity.}\] Further question Wilf about 'Money-Changing Problem' has positive answer for all semigroups multiplicity $[p,2p]$. In particular, this holds semigroup generated not less than $p$. The latter special case was already shown in previous paper.

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ژورنال

عنوان ژورنال: International Journal of Algebra and Computation

سال: 2021

ISSN: ['0218-1967', '1793-6500']

DOI: https://doi.org/10.1142/s0218196721500259