“…, n e + j } j≥0 seem to change periodically with j, for j ≫ 0. This goes in the same direction as a recent number of other results about eventually periodic properties in this shifted family, see [16], [32], [14], [30], [4], [24]. Using [29], we prove in Theorem 3.2 that given n 1 < n 2 < n 3 and letting H j = n 1 + j, n 2 + j, n 3 + j we have res(H j ) = res(H j+(n 3 −n 1 ) ) for all j ≫ 0.…”