Authors and affiliations
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.
- Recurrence relations
- Integer sequences
- Primary 11B50
- Secondary 65Q30, 11Y05, 11Y11
- Ashbacher, C. Pluckings from the Tree of Smarandache Sequences and Functions, American Research Press, 1998.
- Bressoud, D. M. Factorization and Primality Testing, Springer-Verlag, NY, 1989.
- ] Chabert, J. L., É. Barbin, A history of algorithms, Springer, 1994.
- Courant, R., H. Robbins, What is mathematics?, Oxford University Press, 1996 (second edition).
- Dumitrescu, C., V. Seleacu, Some Notions and Questions in Number Theory, Vol. 1, Erhus Publ.,Glendale, 1994.
- Kashihara, K. Comments and topics on Smarandache’s notions and problems, Erhus Univ. Press,1996, 25.
- Ripà, M. On prime factors in old and new sequences of integers, http://vixra.org/abs/1101.0092, 2011.
- Sloane, N. J. A. The Online Encyclopedia of Integer Sequences, http://www.research.att.com/~njas/sequences, 2011.
- Smarandache, F. Only problems, not solutions!, Xiquan Publ. House, Phoenix-Chicago, 1993 (fourth edition).
- Smarandache, F. Properties of the Numbers, University of Craiova Archives, Arizona State University Special Collections, Tempe, AZ, 1975.
- Stephan, R. W. Factors and Primes in Two Smarandache Sequences, Smarandache Notions Journal, Vol. 9, No. 1–2, 1998 (second edition).
- Vassilev-Missana, M., K. Atanassov, Some Smarandache Problems, Hexis, 2004.
Cite this paper
Ripà , M., & Dalmasso, E. (2012). Patterns related to the Smarandache circular sequence primality problem, Notes on Number Theory and Discrete Mathematics, 18(1), 29-48.