On the Bi-Periodic Mersenne Sequence

Ozkan Kizilirmak, Gul; Taşcı, Dursun

doi:10.33401/fujma.1078410

On the Bi-Periodic Mersenne Sequence

Gul Ozkan Kizilirmak, (Gazi Üniversitesi, Fen Fakültesi, Matematik Bölümü, Ankara, Türkiye)

Dursun TAŞÇI (Gazi Üniversitesi, Fen Fakültesi, Matematik Bölümü, Ankara, Türkiye)

Fundamental journal of mathematics and applications (Online)

1 0

Yıl: 2022 Cilt: 5 Sayı: 3 Sayfa Aralığı: 160 - 167 Metin Dili: İngilizce DOI: 10.33401/fujma.1078410 İndeks Tarihi: 23-09-2022

On the Bi-Periodic Mersenne Sequence

Öz:

In this paper, the bi-periodic Mersenne sequence, which is a generalization of the Mersenne sequence, is defined. The characteristic function, generating function and Binet’s formula for this sequence are obtained. Also, by using Binet’s formula, some important identities and properties for the bi-periodic Mersenne sequence are presented.

Anahtar Kelime: Binet formula Catalan identity Generating function Mersenne numbers

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] E. Özkan, A. Aydoğdu, İ. Altun, Some identities for a family of Fibonacci and Lucas numbers, J. Math. Stat. Sci., 3 (2017), 295-303.
[2] S. Çelik, İ. Durukan, E. Özkan, New recurrences on Pell numbers, Pell-Lucas numbers, Jacobsthal numbers, and Jacobsthal-Lucas numbers, Chaos Solitons Fractals,150 (2021), 111173.
[3] E. Özkan, N. Ş . Yilmaz, A. Włoch, On F3(k,n)-numbers of the Fibonacci type, Bol. Soc. Mat. Mex.,27 (2021), 77.
[4] T. Koshy, Pell and Pell–Lucas Numbers with Applications, Springer, New York, 2014.
[5] E. Özkan, M. Uysal, Mersenne-Lucas hybrid numbers, Math. Montisnigri, 52 (2021), 17-29.
[6] P. Catarino, H. Campos, P. Vasco, On the Mersenne sequence, Ann. Math. Inform., 46 (2016),37-53.
[7] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc., New York, 2001.
[8] A. F. Horadam, A generalized Fibonacci sequence, Amer. Math. Monthly, 68 (1961), 455-459.
[9] G. Özkan Kızılırmak, On some identities and Hankel matrices norms involving new defined generalized modified Pell numbers, J. New Results Sci., 10 (2021), 60-66.
[10] G. Bilgici, New generalizations of Fibonacci and Lucas numbers, Appl. Math. Sci., 8 (2014), 1429-1437.
[11] S. Falcon, A. Plaza, On the Fibonacci k-numbers, Chaos Solitions Fractals, 32 (2007), 1615-1624.
[12] A. Szynal-Liana, A. Włoch, I. Włoch, On generalized Pell numbers generated by Fibonacci and Lucas numbers, Ars Combin., 115 (2014), 411-423.
[13] N. Yılmaz, A. Aydog˘du, E. Özkan, Some properties of k-generalized Fibonacci numbers, Math. Montisnigri, 50 (2021), 73-79.
[14] P. Catarino, On some identities for k-Fibonacci sequence, Int. J. Contemp. Math. Sci., 9 (2014), 37- 42.
[15] S. P. Pethe, C. N. Phadte, A generalization of the Fibonacci sequence, Appl. Fibonacci Numbers, 5 (1992), 465-472.
[16] O. M. Yayenie, A. Edson, New generalization of Fibonacci sequences and extended Binet’s formula, Integers, 9 (2009), 639-654.
[17] D. Tasci, E. Sevgi, Bi-periodic Balancing numbers, J. Sci. Arts, 1 (2020), 75-84.
[18] S. Uygun, E. Owusu, A new generalization of Jacobsthal Lucas numbers, J. Adv. Math. Comput. Sci., 7 (2016), 28-39.
[19] J. L. Ramirez, Bi-periodic incomplete Fibonacci sequences, Ann. Math. Inform., 42 (2013), 83–92.
[20] S. Uygun, H. Karatas, A new generalization of Pell-Lucas numbers (Bi-periodic Pell-Lucas sequence), Commun. Math. Appl.,10 (2019), 469–479.

APA	Ozkan Kizilirmak G, Taşcı D (2022). On the Bi-Periodic Mersenne Sequence. , 160 - 167. 10.33401/fujma.1078410
Chicago	Ozkan Kizilirmak Gul,Taşcı Dursun On the Bi-Periodic Mersenne Sequence. (2022): 160 - 167. 10.33401/fujma.1078410
MLA	Ozkan Kizilirmak Gul,Taşcı Dursun On the Bi-Periodic Mersenne Sequence. , 2022, ss.160 - 167. 10.33401/fujma.1078410
AMA	Ozkan Kizilirmak G,Taşcı D On the Bi-Periodic Mersenne Sequence. . 2022; 160 - 167. 10.33401/fujma.1078410
Vancouver	Ozkan Kizilirmak G,Taşcı D On the Bi-Periodic Mersenne Sequence. . 2022; 160 - 167. 10.33401/fujma.1078410
IEEE	Ozkan Kizilirmak G,Taşcı D "On the Bi-Periodic Mersenne Sequence." , ss.160 - 167, 2022. 10.33401/fujma.1078410
ISNAD	Ozkan Kizilirmak, Gul - Taşcı, Dursun. "On the Bi-Periodic Mersenne Sequence". (2022), 160-167. https://doi.org/10.33401/fujma.1078410

APA	Ozkan Kizilirmak G, Taşcı D (2022). On the Bi-Periodic Mersenne Sequence. Fundamental journal of mathematics and applications (Online), 5(3), 160 - 167. 10.33401/fujma.1078410
Chicago	Ozkan Kizilirmak Gul,Taşcı Dursun On the Bi-Periodic Mersenne Sequence. Fundamental journal of mathematics and applications (Online) 5, no.3 (2022): 160 - 167. 10.33401/fujma.1078410
MLA	Ozkan Kizilirmak Gul,Taşcı Dursun On the Bi-Periodic Mersenne Sequence. Fundamental journal of mathematics and applications (Online), vol.5, no.3, 2022, ss.160 - 167. 10.33401/fujma.1078410
AMA	Ozkan Kizilirmak G,Taşcı D On the Bi-Periodic Mersenne Sequence. Fundamental journal of mathematics and applications (Online). 2022; 5(3): 160 - 167. 10.33401/fujma.1078410
Vancouver	Ozkan Kizilirmak G,Taşcı D On the Bi-Periodic Mersenne Sequence. Fundamental journal of mathematics and applications (Online). 2022; 5(3): 160 - 167. 10.33401/fujma.1078410
IEEE	Ozkan Kizilirmak G,Taşcı D "On the Bi-Periodic Mersenne Sequence." Fundamental journal of mathematics and applications (Online), 5, ss.160 - 167, 2022. 10.33401/fujma.1078410
ISNAD	Ozkan Kizilirmak, Gul - Taşcı, Dursun. "On the Bi-Periodic Mersenne Sequence". Fundamental journal of mathematics and applications (Online) 5/3 (2022), 160-167. https://doi.org/10.33401/fujma.1078410