Journal of Integer Sequences, Vol. 21 (2018), Article 18.1.8

Curious Bounds for Floor Function Sums

Thotsaporn Thanatipanonda and Elaine Wong
Science Division
Mahidol University International College
Nakhon Pathom, 73170


Jacobsthal was the first to study a certain kind of sum of floor functions. His work was followed by that of Carlitz, Grimson, and Tverberg. More recently, Onphaeng and Pongsriiam proved some sharp upper and lower bounds for the sums of Jacobsthal and Tverberg. In this paper, we devise concise formulas for these sums, which we then use to prove the upper and lower bounds claimed by Tverberg. Furthermore, we present conjectural lower and upper bounds for these sums.

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Received September 19 2017; revised versions received February 14 2018; February 16 2018; February 18 2018. Published in Journal of Integer Sequences, February 23 2018.

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