A STUDY ON GENERALIZED 5-PRIMES NUMBERS


Abstract views: 155 / PDF downloads: 215

Authors

DOI:

https://doi.org/10.26900/jsp.4.017%20

Keywords:

5-primes numbers, Lucas 5-primes numbers, generalized Pentanacci numbers, modied 5-primes numbers

Abstract

In this paper, we introduce the generalized 5-primes numbers sequences and we deal with, in detail, three special cases which we call them 5-primes, Lucas 5-primes and modified 5-primes sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

Downloads

Download data is not yet available.

References

[1] Howard, F.T., Saidak, F., Zhou’s Theory of Constructing Identities, Congress Numer. 200, 225-237, 2010.
[2] Kalman, D., Generalized Fibonacci Numbers By Matrix Methods, Fibonacci Quarterly, 20(1), 73-76, 1982.
[3] Kiliç, E., Stanica, P., A Matrix Approach for General Higher Order Linear Recurrences, Bulletin of the Malaysian Mathematical Sciences Society, (2) 34(1), 51.67, 2011.
[4] Melham, R. S., Some Analogs of the Identity , F_n^2+F_(n+1)^2=F_(2n+1)^2 Fibonacci Quarterly, 305-311, 1999.
[5] Natividad, L. R., On Solving Fibonacci-Like Sequences of Fourth, Fifth and Sixth Order, International Journal of Mathematics and Computing, 3 (2), 2013.
[6] Rathore, G.P.S., Sikhwal, O., Choudhary, R., Formula for finding nth Term of Fibonacci-Like Sequence of Higher Order, International Journal of Mathematics And its Applications, 4 (2-D), 75-80, 2016.
[7] Sloane, N.J.A., The on-line encyclopedia of integer sequences, http://oeis.org/
[8] Soykan, Y., Simson Identity of Generalized m-step Fibonacci Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2), 45-56, 2019.
[9] Soykan, Y., Sum Formulas For Generalized Fifth-Order Linear Recurrence Sequences, Journal of Advances in Mathematics and Computer Science, 34(5), 1-14, 2019, Article no.JAMCS.53303, ISSN: 2456-9968, DOI: 10.9734/JAMCS/2019/v34i530224.  

Downloads

Published

2020-08-05 — Updated on 2020-08-06

How to Cite

SOYKAN, Y. (2020). A STUDY ON GENERALIZED 5-PRIMES NUMBERS. HEALTH SCIENCES QUARTERLY, 4(3), 185–202. https://doi.org/10.26900/jsp.4.017

Issue

Vol. 4 No. 3 (2020)

Section

Letter to the Editor

License

Copyright (c) 2020 Holistence Publications

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

When the  article is accepted for publication in the HSQ authors transfer all copyright in the article to the Holistence Academy Ar-Ge Yazılım Yayıncılık Eğitim Danışmanlık ve Organizasyon Ticaret Ltd. Şti.The authors reserve all proprietary right other than copyright, such as patent rights. 

Everyone who is listed as an author in this article should have made a substantial, direct, intellectual contribution to the work and should take public responsibility for it.

This paper contains works that have not previously published or not under consideration for publication in other journals.