Authors and affiliations
In this article we show that the following Pillai’s conjecture pn 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.
- Pillai’s conjecture
- Gaps between consecutive primes
- General sequences
- Sequence of perfect powers
- 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.
Cite this paperAPA
Jakimczuk, R. (2017). On a Pillai’s Conjecture and Gaps between Consecutive Primes. Notes on Number Theory and Discrete Mathematics, 23(3), 60-72.Chicago
Jakimczuk, Rafael. “On a Pillai’s Conjecture and Gaps between Consecutive Primes.” Notes on Number Theory and Discrete Mathematics 23, no. 3 (2017): 60-72.MLA
Jakimczuk, Rafael. “On a Pillai’s Conjecture and gaps between consecutive primes.” Notes on Number Theory and Discrete Mathematics 23.3 (2017): 60-72. Print.