Given relative prime positive integers A=(a1β,a2β,...,anβ), the
Frobenius number g(A) is the largest integer not representable as a linear
combination of the aiβ's with nonnegative integer coefficients. We find the
``Stable" property introduced for the square sequence A=(a,a+1,a+22,β¦,a+k2) naturally extends for A(a)=(a,ha+d,ha+b2βd,...,ha+bkβd). This gives a
parallel characterization of g(A(a)) as a ``congruence class function" modulo
bkβ when a is large enough. For orderly sequence B=(1,b2β,β¦,bkβ), we
find good bound for a. In particular we calculate g(a,ha+dB) for
B=(1,2,b,b+1,2b), B=(1,b,2bβ1) and B=(1,2,...,k,K)