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 fλ(p) the largest integer which cannot be written as a sum of primes from [p,p + λp]. Then fλ(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.

中文翻译：

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关于某些数值半群的 Frobenius 数

让0 < λ ≤ 1,λ∉{2 4, 2 7, 2 10, 2 13,…}, 是一个真实的和p一个素数，有[p,p + λp]至少包含两个素数。表示为Fλ(p)不能写成素数和的最大整数[p,p + λp]. 然后 Fλ(p) ～ 2 + 2 λ ⋅ p,作为 p 走向无穷大。 Wilf 关于“货币兑换问题”的进一步问题对所有多重性半群都有一个肯定的答案p包含来自的素数[p, 2p]. 特别是，这适用于由不小于所有素数生成的半群p. 后一种特殊情况已经在之前的论文中展示过。