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This article will be started with a fundamental observation on consecutive non-negative integers. Based on the observation, we will demonstrate that the sequence of non-negative integers is regarded as a uniformly distributed sequence in the ring of the p-adic integers. As a result, the sequence provides us with a faster rate of convergence than the one obtained by simply applying law of the iterated logarithm. [ABSTRACT FROM AUTHOR]

Defines a class of s-dimensional uniformly distributed sequences called the generalized van der Corput sequence. Introduction of the generalized number system based on an expanding integer matrix; Application to numerical integration problems; Sample equation.