Two Algorithms for Exact Evaluation of the Newman Digit Sum and the Sharp Extimates
نویسنده
چکیده
We give two simple algorithms for the exact evaluation of the sum S(x) = 0≤n<x;n≡0(mod3) (−1) σ(n) , where σ(n) is the binary digit sum of n and obtain the sharp estimates for x −λ S(x), λ = ln 3 ln 4 .
منابع مشابه
Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs
In $1994,$ degree distance of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the multiplicative version of degree distance and multiplicative ver...
متن کاملDesign and Synthesis of High Speed Low Power Signed Digit Adders
Signed digit (SD) number systems provide the possibility of constant-time addition, where inter-digit carry propagation is eliminated. Such carry-free addition is primarily a three-step process; adding the equally weighted SDs to form the primary sum digits, decomposing the latter to interim sum digits and transfer digits, which commonly belong to {–1, 0, 1}, and finally adding the tra...
متن کاملA comparison of algorithms for minimizing the sum of earliness and tardiness in hybrid flow-shop scheduling problem with unrelated parallel machines and sequence-dependent setup times
In this paper, the flow-shop scheduling problem with unrelated parallel machines at each stage as well as sequence-dependent setup times under minimization of the sum of earliness and tardiness are studied. The processing times, setup times and due-dates are known in advance. To solve the problem, we introduce a hybrid memetic algorithm as well as a particle swarm optimization algorithm combine...
متن کاملEffect of Objective Function on the Optimization of Highway Vertical Alignment by Means of Metaheuristic Algorithms
The main purpose of this work is the comparison of several objective functions for optimization of the vertical alignment. To this end, after formulation of optimum vertical alignment problem based on different constraints, the objective function was considered as four forms including: 1) the sum of the absolute value of variance between the vertical alignment and the existing ground; 2) the su...
متن کاملA Comparative Study of Exact Algorithms for the Two Dimensional Strip Packing Problem
In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...
متن کامل