Rafael Jakimczuk

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 23, 2017, Number 3, Pages 60—72

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## Details

### Authors and affiliations

Rafael Jakimczuk

*División Matemática, Universidad Nacional de Luján
Buenos Aires, Argentina
*

### Abstract

In this article we show that the following Pillai’s conjecture *p _{n}* is the

*n*-th prime number)

can be established in terms of gaps between consecutive primes. We also study general sequences that have this property. We call these sequences Pillai sequences. We prove that the sequence of perfect powers is a Pillai-sequence.

### Keywords

- Pillai’s conjecture
- Gaps between consecutive primes
- General sequences
- Sequence of perfect powers

### AMS Classification

- 11A99
- 11B99

### References

- Chowla, S. (1965) The Riemann Hypothesis and Hilbert’s Tenth Problem, Gordon andBreach, Science Publishers.
- Jakimczuk, R. (2010) Functions of slow increase and integer sequences, Journal of Integer Sequences, 13, Article 10.1.1.
- Jakimczuk, R. (2015) Some results of the difference between consecutive perfect powers, Gulf Journal of Mathematics, 3(3), 9–32.
- Jakimczuk, R. (2012) Asymptotic formulae for the
*n*-th perfect power, Journal of Integer Sequences, 15, Article 12.5.5. - Rey Pastor, J., Pi Calleja, P. & Trejo, C. (1969) Analisis Matematico, Editorial Kapelusz.

## Related papers

## Cite this paper

APAJakimczuk, R. (2017). On a Pillai’s Conjecture and Gaps between Consecutive Primes. Notes on Number Theory and Discrete Mathematics, 23(3), 60-72.

ChicagoJakimczuk, Rafael. “On a Pillai’s Conjecture and Gaps between Consecutive Primes.” Notes on Number Theory and Discrete Mathematics 23, no. 3 (2017): 60-72.

MLAJakimczuk, Rafael. “On a Pillai’s Conjecture and gaps between consecutive primes.” Notes on Number Theory and Discrete Mathematics 23.3 (2017): 60-72. Print.