Let (an),(bn) be linear recursive sequences of integers with characteristic polynomials A(X),B(X)∈Z[X] respectively. Assume that A(X) has a dominating and simple real root α, while B(X) has a pair of conjugate complex dominating and simple roots β,β̄. Assume further that α,β,α/β and β̄/β are not roots of unity and δ=log|β|/log|α|∈Q. Then there are effectively computable constants c0,c1>0 such that the inequality |an−bm|>|an|1−(c0log2n)/nholds for all n,m∈Z≥02 with max{n,m}>c1. We present c0 explicitly.