Digit-Coefficient Tester

We use P(x) ∈ Z[x] (monic) and assume a_k ≥ 0 for all k, where a_k is the coefficient of x^k in 1 / P((1-mx)/x). The scan runs over m = m_min..m_max. The digit d_k(n) is the k-th digit after the decimal point of 1 / P(n) in base (n + m), using 1-based indexing (k = 1 is the first digit). The scan skips cases where a_k or a_k+1 is negative or non-integer. In random mode we require a_k ≥ 0 and integer for k ≤ k_max + 1 and all m in the scan. The test condition is n ≥ m² + k + a_k+1. In x^j mode we test: if k ≥ m(j−1)+j−2 and C_k < n, then d_k(n)=C_k+1.