patterns related to the smarandache circular sequence primality problem

21
 PATTERNS RELATED TO THE SMARANDACHE CIRCULAR SEQUENCE PRIMALITY PROBLEM  Marco Ripà Graduate student, Roma Tre University, Rome, Italy E-mail: [email protected] Abstract In this paper, we show the internal relations among the elements of the circular sequence (1,12,21,123,231,31 2,1234,2341 ,…). 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 anot her 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.

Upload: marco-ripa

Post on 08-Apr-2018

220 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 1/21

Page 2: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 2/21

Page 3: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 3/21

Page 4: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 4/21

Page 5: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 5/21

Page 6: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 6/21

Page 7: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 7/21

Page 8: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 8/21

Page 9: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 9/21

Page 10: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 10/21

Page 11: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 11/21

Page 12: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 12/21

Page 13: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 13/21

Page 14: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 14/21

Page 15: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 15/21

Page 16: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 16/21

Page 17: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 17/21

Page 18: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 18/21

Page 19: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 19/21

Page 20: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 20/21

Page 21: Patterns Related to the Smarandache Circular Sequence Primality Problem

8/7/2019 Patterns Related to the Smarandache Circular Sequence Primality Problem

http://slidepdf.com/reader/full/patterns-related-to-the-smarandache-circular-sequence-primality-problem 21/21