201. The Frobenius formula for A=(a,ha+d,ha+b2d,...,ha+bkd).
- Author
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Liu, Feihu, Xin, Guoce, Ye, Suting, and Yin, Jingjing
- Abstract
Given a set of positive integers A = (a 1 , a 2 , ... , a n) whose greatest common divisor is 1, the Frobenius number g(A) is the largest integer not representable as a linear combination of the a i 's with nonnegative integer coefficients. We find the stable property introduced for the square sequence A = (a , a + 1 , a + 2 2 , ⋯ , a + k 2) naturally extends for A (a) = (a , h a + d B) = (a , h a + d , h a + b 2 d , ... , h a + b k d) . This gives a parallel characterization of g(A(a)) as a "congruence class function" modulo b k when a is large enough. For orderly sequence B = (1 , b 2 , ⋯ , b k) , we find good bound for a. In particular we calculate g (a , h a + d B) for B = (1 , 2 , b , b + 1) , B = (1 , 2 , b , b + 1 , 2 b) , B = (1 , b , 2 b - 1) , and B = (1 , 2 , ... , k , K) . [ABSTRACT FROM AUTHOR]
- Published
- 2024
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