Patterns related to the Smarandache circular sequence primality problem

Abstract In this paper, we show the internal relations among the elements of the circular sequence (1,12,21,123,231,312,1234,2341,…). We illustrate one method to minimize the number of the “candidate prime numbers ” up to a given term of the sequence. So, having chosen a particular prime divisor, it is possible to analyze only a fixed number of the smallest terms belonging to a given range, thus providing the distribution of that prime factor in a larger set of elements. Finally, we combine these results with another one, also expanding the study to a few new integer sequences related to the circular one