Discatenated and lacunary recurrences

Hakan Akkuş, Ömür Deveci, Engin Özkan and Anthony G. Shannon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 1, Pages 8–19
DOI: 10.7546/nntdm.2024.30.1.8-19
Full paper (PDF, 944 Kb)

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Authors and affiliations

Hakan Akkuş
Department of Mathematics, Graduate School of Natural and Applied Sciences, Erzincan Binali Yıldırım University
Yalnızbağ Campus, 24100, Erzincan, Türkiye

Ömür Deveci
Department of Mathematics, Faculty of Sciences Arts, Kafkas University
36100 Kars, Türkiye

Engin Özkan
Department of Mathematics, Faculty of Sciences Arts, Erzincan Binali Yıldırım University
Yalnızbağ Campus, 24100, Erzincan, Türkiye

Anthony G. Shannon
Warrane College, The University of New South Wales
Kensington, NSW 2033, Australia

Abstract

Recursive sequences with gaps have been studied previously. This paper considers some elementary properties of such sequences where the gaps have been created on a regular basis from sequence to sequence – ‘discatenated’ (systematic gaps) and ‘lacunary’ (general gaps). In particular, their generating functions are developed in order to open up their general terms and relations with other properties.

Keywords

• Fibonacci numbers
• Lucas sequences
• Lacunary
• Primordial sequences
• Recurrence relations

2020 Mathematics Subject Classification

• 11B39
• 11B0F

References

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Manuscript history

• Received: 8 January 2023
• Revised: 14 February 2023
• Accepted: 17 February 2024
• Online First: 23 February 2024

Copyright information

Ⓒ 2024 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).