Papers › On the Frobenius number of certain numerical semigroups
On the Frobenius number of certain numerical semigroups
Michael Hellus, Anton Rechenauer, Rolf Waldi
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Let 0<λ≤1, λ∉{2/4, 2/7, 2/10, 2/13, …}, be a real and p a prime number, with [p,p+λp] containing at least two primes. Denote by f_λ(p) the largest integer which cannot be written as a sum of primes from [p,p+λp]. Then f_λ(p)∼⌊2+2/λ⌋·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.
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