Patterns related to the Smarandache circular sequence primality problem

Marco Ripà and Emanuele Dalmasso
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 18, 2012, Number 1, Pages 29–48
Full paper (PDF, 736 Kb)

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Authors and affiliations

Marco Ripà

Graduate student, Roma Tre University, Rome, Italy

Emanuele Dalmasso

Ph.D. Computer Science Engineering, Turin Polytechnic, Turin, Italy

Abstract

In this paper, we show the internal relations among the elements of the circular sequence (1, 12, 21, 123, 231, 312, 1234, 3412, …). 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.

Keywords

• Recurrence relations
• Factorization
• Patterns
• Integer sequences
• Permutations
• Primes

AMS Classification

• Primary 11B50
• Secondary 65Q30, 11Y05, 11Y11

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