Last Updated: 2017/8/10
The sums of floor functions have been studied by Jacobsthal, Carlitz, Grimson and more recently by Tverberg. In 2017, Onphaeng and Pongsriiam proved some sharp upper and lower bounds for the sums of Jacobsthal and Tverberg. In this paper, we formulate a concise formula for the sums and then use it to give proofs of the upper and lower bounds that were claimed by Tverberg. Furthermore, we conjecture all of the bounds related to this kind of problem.