J. V. Leyendekkers and A. G. Shannon

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 3, Pages 77–83

DOI: 10.7546/nntdm.2018.24.3.77-83

**Full paper (PDF, 87 Kb)**

## Details

### Authors and affiliations

J. V. Leyendekkers

*Faculty of Science, The University of Sydney, NSW 2006, Australia
*

A. G. Shannon

*Warrane College, The University of New South Wales, NSW 2033, Australia
Emeritus Professor, University of Technology Sydney, NSW 2007, Australia
*

### Abstract

Primes are considered in three sequences, of which two are exclusive to specific primes. These sequences have the integers represented in the form *nR* where *R* is the right-end-digit of the prime and *n* represents the remaining left digits which are given by linear equations.

### Keywords

- Right-end-digits
- Integer structure analysis
- Modular rings
- Prime-indexed numbers
- Fibonacci numbers
- Mersenne numbers

### 2010 Mathematics Subject Classification

- 11A51
- 11A07

### References

- Cattani, C., & Ciancio, A. (2016) On the fractal distribution of primes and prime-indexed primes by the binary image analysis. Physica A: Statistical Mechanics and Its Applications. 460 (1), 222–229.
- Lemke Oliver, R. J., & Soundararajan, K. (2016) Unexpected biases in the distribution of consecutive primes. Preprint. Available online: https://arxiv.org/abs/1603.03720
- Leyendekkers, J. V., Shannon, A. G., & Rybak, J. M. (2007) Pattern Recognition: Modular Rings and Integer Structure. North Sydney: Raffles KvB Monograph No.9.
- Leyendekkers, J. V., & Shannon, A. G. (1998) The characteristics of primes and other integers within Modular Ring Z
_{4}and in Class 1_{4}.*Notes on Number Theory and Discrete Mathematics*, 4 (1), 1–17. - Leyendekkers, J. V., & Shannon, A. G. (1998) The characteristics of primes and other integers within Modular Ring Z
_{4}and in Class 3_{4}.*Notes on Number Theory and Discrete Mathematics*, 4 (1), 18–37. - Leyendekkers, J. V., & Shannon, A. G. (2002) Constraints on powers within the modular ring Z
_{4}Part 1: Even powers.*Notes on Number Theory and Discrete Mathematics*, 8 (2), 41–57. - Leyendekkers, J. V., & Shannon, A. G. (2004) Extensions of Euler’s prime generating functions.
*Notes on Number Theory and Discrete Mathematics*, 10 (4), 100–105. - Leyendekkers, J. V., & Shannon, A. G. (2008) Analysis of primes using REDs (right-enddigits) and integer structure.
*Notes on Number Theory and Discrete Mathematics*, 14 (3), 1–10. - Leyendekkers, J. V., & Shannon, A. G. (2008) The identification of rows of primes in the modular ring Z
_{6}.*Notes on Number Theory and Discrete Mathematics*, 14 (4), 10–15. - Leyendekkers, J. V., A.G. Shannon, C.K. Wong. 2009) Spectra of primes. Proceedings of the Jangjeon Mathematical Society. 12 (1), 1–10.
- Leyendekkers, J. V., & Shannon, A. G. (2014) Fibonacci Numbers with Prime Subscripts: Digital Sums for Primes versus Composites.
*Notes on Number Theory and Discrete Mathematics*, 20(3), 45–49. - Knott, R. (2011) The Fibonacci Numbers, Available online: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibtable.html
- Leyendekkers, J. V., & Shannon, A. G. (2005) Fermat and Mersenne Numbers.
*Notes on Number Theory and Discrete Mathematics*, 11 (4), 17–24.

## Related papers

## Cite this paper

Leyendekkers, J. V. & Shannon, A. G. (2018). Prime sequences. *Notes on Number Theory and Discrete Mathematics*, 24(3), 77-83, DOI: 10.7546/nntdm.2018.24.3.77-83.