Explicit formulas for F(A) and g(A) are obtained for the semigroup generated by A = (a, ba + d, b²a + ((b²-1)/(b-1))d, ..., b^k a + ((b^k-1)/(b-1))d) when a ≥ k-1 - (d-1)/(b-1), with simplifications for Mersenne, Thabit, repunit, and partial results for Proth semigroups.
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math.NT 2years
2023 2verdicts
UNVERDICTED 2representative citing papers
Reduces Apéry set of semigroup quotients to minimization when p divides a1, giving closed Frobenius formulas for almost arithmetic progression generators and partially solving a prior open problem.
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On the Frobenius Number and Genus of a Collection of Semigroups Generalizing Repunit Numerical Semigroups
Explicit formulas for F(A) and g(A) are obtained for the semigroup generated by A = (a, ba + d, b²a + ((b²-1)/(b-1))d, ..., b^k a + ((b^k-1)/(b-1))d) when a ≥ k-1 - (d-1)/(b-1), with simplifications for Mersenne, Thabit, repunit, and partial results for Proth semigroups.
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On quotients of numerical semigroups for almost arithmetic progressions
Reduces Apéry set of semigroup quotients to minimization when p divides a1, giving closed Frobenius formulas for almost arithmetic progression generators and partially solving a prior open problem.