Srivastava, PranjalPranjalSrivastavaThakkar, DharaDharaThakkar2025-08-312025-08-312024-01-01[9783031522123]10.1007/978-3-031-52213-0_122-s2.0-85184125612http://repository.iitgn.ac.in/handle/IITG2025/29162Let n be a positive integer greater than 2. We define the Proth numerical semigroup, P<inf>k</inf>(n), generated by {k2n+i+1∣i∈N}, where k is an odd positive number and k&lt; 2 ⁿ. In this paper, we introduce the Frobenius problem for the Proth numerical semigroup P<inf>k</inf>(n) and give formulas for the embedding dimension of P<inf>k</inf>(n). We solve the Frobenius problem for P<inf>k</inf>(n) by giving a closed formula for the Frobenius number. Moreover, we show that P<inf>k</inf>(n) has an interesting property such as being Wilf.falseApéry Set | Combinatorial techniques | Frobenius problem | Numerical semigroup | Proth Number | pseudo-Frobenius number | type | Wilf’s conjectureConference Paper16113349162-17520242cpBook Series1