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On the Bi-Periodic Mersenne Sequence

Yıl 2022, Cilt: 5 Sayı: 3, 160 - 167, 23.09.2022
https://doi.org/10.33401/fujma.1078410

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.

Kaynakça

  • [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.
Yıl 2022, Cilt: 5 Sayı: 3, 160 - 167, 23.09.2022
https://doi.org/10.33401/fujma.1078410

Öz

Kaynakça

  • [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.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Gül Özkan Kızılırmak 0000-0003-3263-8685

Dursun Taşçı 0000-0001-8357-4875

Yayımlanma Tarihi 23 Eylül 2022
Gönderilme Tarihi 24 Şubat 2022
Kabul Tarihi 2 Mayıs 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 3

Kaynak Göster

APA Özkan Kızılırmak, G., & Taşçı, D. (2022). On the Bi-Periodic Mersenne Sequence. Fundamental Journal of Mathematics and Applications, 5(3), 160-167. https://doi.org/10.33401/fujma.1078410
AMA Özkan Kızılırmak G, Taşçı D. On the Bi-Periodic Mersenne Sequence. Fundam. J. Math. Appl. Eylül 2022;5(3):160-167. doi:10.33401/fujma.1078410
Chicago Özkan Kızılırmak, Gül, ve Dursun Taşçı. “On the Bi-Periodic Mersenne Sequence”. Fundamental Journal of Mathematics and Applications 5, sy. 3 (Eylül 2022): 160-67. https://doi.org/10.33401/fujma.1078410.
EndNote Özkan Kızılırmak G, Taşçı D (01 Eylül 2022) On the Bi-Periodic Mersenne Sequence. Fundamental Journal of Mathematics and Applications 5 3 160–167.
IEEE G. Özkan Kızılırmak ve D. Taşçı, “On the Bi-Periodic Mersenne Sequence”, Fundam. J. Math. Appl., c. 5, sy. 3, ss. 160–167, 2022, doi: 10.33401/fujma.1078410.
ISNAD Özkan Kızılırmak, Gül - Taşçı, Dursun. “On the Bi-Periodic Mersenne Sequence”. Fundamental Journal of Mathematics and Applications 5/3 (Eylül 2022), 160-167. https://doi.org/10.33401/fujma.1078410.
JAMA Özkan Kızılırmak G, Taşçı D. On the Bi-Periodic Mersenne Sequence. Fundam. J. Math. Appl. 2022;5:160–167.
MLA Özkan Kızılırmak, Gül ve Dursun Taşçı. “On the Bi-Periodic Mersenne Sequence”. Fundamental Journal of Mathematics and Applications, c. 5, sy. 3, 2022, ss. 160-7, doi:10.33401/fujma.1078410.
Vancouver Özkan Kızılırmak G, Taşçı D. On the Bi-Periodic Mersenne Sequence. Fundam. J. Math. Appl. 2022;5(3):160-7.

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