A Short Computer Program That Computes in the Limit a Non-Computable Function from N to N

For n∈N, f(n) denotes the smallest b∈N such that if a system of equations S⊆{1=x_k, x_i+x_j=x_k, x_i·x_j=x_k: i,j,k∈{0,...,n}} has a solution in Nⁿ⁺¹, then S has a solution in {0,...,b}ⁿ⁺¹. The author proved earlier that the function f:N→N is computable in the limit and eventually dominates every computable function g:N→N. We present a short program in MuPAD which for n∈N prints the sequence {f_i(n)}ᵢ₌₀^∞ of non-negative integers converging to f(n). The previously known computer programs by other authors do not compute in the limit non-computable functions from N to N. We present a short program in MuPAD that computes in the limit a function β:N→N of unknown computability which eventually dominates every function δ:N→N with a single-fold Diophantine representation.