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Yıl 2023, Sayı: 054, 62 - 75, 30.09.2023

Fikri Köken Emre Kankal

https://doi.org/10.59313/jsr-a.1251592
Cited By: 1

Öz

Kaynakça

  • [1] OEIS Foundation Inc. (2011). The on-line encyclopedia of integer sequences. http://oeis.org.
  • [2] Koshy T. (2001). Fibonacci and Lucas numbers with applications. John Wiley and Sons Inc, NY.
  • [3] Chen, K.W. (2011). Greatest common divisors in shifted Fibonacci sequences. Journal of Integer Sequences, 14, 11.4.7.
  • [4] Koken, F. (2020). The gcd sequences of the altered Lucas sequences. Annales Mathematicae Silesianae, 34, 2, 222-240. DOI: 10.2478/amsil-2020-0005.
  • [5] Cerin, Z. (2013). On factors of sums of consecutive Fibonacci and Lucas numbers. Annales Mathematicae et Informaticae, 41, 19–25.
  • [6] Tekcan, A., Gezer, B. and Bizim, O. (2007). Some relations on Lucas numbers and their sums. Advanced Studies in Contemporary Mathematics, 15, 195–211.
  • [7] Szalay, L. (2012). Diophantine equations with binary recurrences associated to the Brocard–Ramanujan problem. Portugaliae Mathematica, 69, 3, 213–220.
  • [8] Pongsriiam, P. (2017). Fibonacci and Lucas numbers associated with Brocard-Ramanujan equation. Communications of the Korean Mathematical Society, 32, 3, 511-522.
  • [9] Kankal E. (2023). The thesis of master of science, Necmettin Erbakan University. The Graduate School of Natural And Applied Science, Konya.

ALTERED NUMBERS OF LUCAS NUMBER SQUARED

Yıl 2023, Sayı: 054, 62 - 75, 30.09.2023

Fikri Köken Emre Kankal

https://doi.org/10.59313/jsr-a.1251592
Cited By: 1

Öz

We investigate two types altered Lucas numbers denoted and defined by adding or subtracting a value from the square of the Lucas numbers. We achieve these numbers form as the consecutive products of the Fibonacci numbers. Therefore, consecutive sum-subtraction relations of altered Lucas numbers and their Binet-like formulas are given by using some properties of the Fibonacci numbers. Also, we explore the gcd sequences of r–successive terms of altered Lucas numbers denoted and , , according to the greatest common divisor (gcd) properties of consecutive terms of the Fibonacci numbers. We show that these sequences are periodic or Fibonacci sequences.

Anahtar Kelimeler

Altered Lucas numbers Greatest common divisor (gcd) sequences Fibonacci sequence Lucas sequence

Kaynakça

  • [1] OEIS Foundation Inc. (2011). The on-line encyclopedia of integer sequences. http://oeis.org.
  • [2] Koshy T. (2001). Fibonacci and Lucas numbers with applications. John Wiley and Sons Inc, NY.
  • [3] Chen, K.W. (2011). Greatest common divisors in shifted Fibonacci sequences. Journal of Integer Sequences, 14, 11.4.7.
  • [4] Koken, F. (2020). The gcd sequences of the altered Lucas sequences. Annales Mathematicae Silesianae, 34, 2, 222-240. DOI: 10.2478/amsil-2020-0005.
  • [5] Cerin, Z. (2013). On factors of sums of consecutive Fibonacci and Lucas numbers. Annales Mathematicae et Informaticae, 41, 19–25.
  • [6] Tekcan, A., Gezer, B. and Bizim, O. (2007). Some relations on Lucas numbers and their sums. Advanced Studies in Contemporary Mathematics, 15, 195–211.
  • [7] Szalay, L. (2012). Diophantine equations with binary recurrences associated to the Brocard–Ramanujan problem. Portugaliae Mathematica, 69, 3, 213–220.
  • [8] Pongsriiam, P. (2017). Fibonacci and Lucas numbers associated with Brocard-Ramanujan equation. Communications of the Korean Mathematical Society, 32, 3, 511-522.
  • [9] Kankal E. (2023). The thesis of master of science, Necmettin Erbakan University. The Graduate School of Natural And Applied Science, Konya.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Articles
Yazarlar

Fikri Köken 0000-0002-8304-9525

Emre Kankal Bu kişi benim 0000-0002-2707-5323

Yayımlanma Tarihi 30 Eylül 2023
Gönderilme Tarihi 15 Şubat 2023
Yayımlandığı Sayı Yıl 2023 Sayı: 054

Kaynak Göster

IEEE F. Köken ve E. Kankal, “ALTERED NUMBERS OF LUCAS NUMBER SQUARED”, JSR-A, sy. 054, ss. 62–75, Eylül 2023, doi: 10.59313/jsr-a.1251592.

Cited By

Altered Numbers of Fibonacci Number Squared
Journal of New Theory
https://doi.org/10.53570/jnt.1368751
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