Journal of Integer Sequences, Vol. 14 (2011), Article 11.9.1

Inequalities and Identities Involving Sums of Integer Functions


Mircea Merca
Department of Informatics
Constantin Istrati Technical College
Griviţei 91, 105600 Campina
Romania

Abstract:

The aim of this paper is to present a method of generating inequalities and, under certain conditions, some identities with sums that involve floor, ceiling and round functions. We apply this method to sequences of nonnegative integers that could be turned into periodical sequences.

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(Concerned with sequences A000045 A000975 A001175 A004697 A014785 A014817 A026039 A033113 A033114 A033115 A033116 A033117 A033118 A033119 A033138 A070333 A077854 A088551 A097137 A097138 A097139 A122046 A131941 A153234 A156002 A171965 A172046 A172131 A173196 A173645 A173690 A173691 A173721 A173722 A175287 A175724 A175766 A175780 A175812 A175822 A175826 A175827 A175829 A175831 A175842 A175846 A175848 A175864 A175868 A175869 A175870 A177041 A177100 A177166 A177176 A177189 A177205 A177237 A177239 A177277 A177332 A177337 A177339 A177881 A178222 A178397 A178420 A178452 A178455 A178543 A178577 A178703 A178704 A178706 A178710 A178711 A178719 A178730 A178742 A178744 A178750 A178826 A178827 A178828 A178829 A178872 A178873 A178874 A178875 A178982 A179001 A179006 A179018 A179041 A179042 A179053 A179111 A181120 A181286 A181640.)

Received February 16 2011; revised versions received July 7 2011; September 5 2011. Published in Journal of Integer Sequences, October 16 2011.

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