On Concatenations of Fibonacci and Lucas Numbers

Alan, Murat

doi:10.1007/s41980-021-00668-7

Cited by 9 publications

(3 citation statements)

References 14 publications

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“…Here (𝐹 𝑛 ) be the sequence of Fibonacci numbers and 𝑑 indicates the number of digits of 𝐿 𝑛 and 𝐹 𝑛 . In (Altassan and Alan 2022), after a short time Altassan and Alan deal with the equations 𝐹 𝑛 = 10 𝑑 𝐹 𝑚 + 𝐿 𝑘 𝐹 𝑛 = 10 𝑑 𝐿 𝑚 + 𝐹 𝑘 .…”

Section: Introductionmentioning

confidence: 99%

İki Lucas Sayısının Birleşimi Olan Mulatu Sayıları

ERDUVAN

2023

Afyon Kocatepe University Journal of Sciences and Engineering

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In this paper, we find that all Mulatu numbers, which are concatenations of two Lucas numbers are 11,17,73,118. Let 〖(M_k)〗_(k≥0) and 〖(L_k)〗_(k≥0) be the Mulatu and Lucas sequences. That is, we solve the Diophantine equation M_k=L_m L_n=10^d L_m+L_n in non-negative integers (k,m,n,d), where d denotes the number of digits of L_n. Solutions of this equation are denoted by (k,m,n,d)=(4,1,1,1),(5,1,4,1),(8,4,2,1),(9,1,6,2). In other words, we have the solutions M_4=L_1 L_1=11, M_5=L_1 L_4=17, M_8=L_4 L_2=73, M_9=L_1 L_6=118. The proof based on Baker’s theory and we used linear forms in logarithms and reduction method to solve of this Diophantine equation.

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Section: Introductionmentioning

confidence: 99%

İki Lucas Sayısının Birleşimi Olan Mulatu Sayıları

ERDUVAN

2023

Afyon Kocatepe University Journal of Sciences and Engineering

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“…In fact, they proved that for any binary recurrent sequence of integers t n , there exists only finitely many terms of that sequence which can be written as concatenations of two or more terms of t n under the some mild hypotheses. In [1], the author found all Fibonacci (Lucas) numbers that are concatenations of two Lucas (Fibonacci) numbers. Recently, in [11,18], the authors consider the concatenations of Padovan and Perrin numbers that are third order recurrence sequences.…”

Section: Introductionmentioning

confidence: 99%

“…In [1], the author found all Fibonacci (Lucas) numbers that are concatenations of two Lucas (Fibonacci) numbers. Recently, in [11,18], the authors consider the concatenations of Padovan and Perrin numbers that are third order recurrence sequences.…”

Section: Introductionmentioning

confidence: 99%

Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences

Altassan

Alan

2023

Mathematics

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In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the k-generalized Fibonacci sequence which are almost repdigits. In particular, we find all k-generalized Fibonacci numbers which are powers of 10 as a special case of almost repdigits. In the second part of the paper, by using the roots of the characteristic polynomial of the k-generalized Fibonacci sequence, we introduce k-generalized tiny golden angles and show the feasibility of this new type of angles in application to magnetic resonance imaging.

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Padovan numbers that are concatenations of a Padovan number and a Perrin number

Güney Duman

2024

Period Math Hung

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On Concatenations of Fibonacci and Lucas Numbers

Cited by 9 publications

References 14 publications

İki Lucas Sayısının Birleşimi Olan Mulatu Sayıları

İki Lucas Sayısının Birleşimi Olan Mulatu Sayıları

Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences

Padovan numbers that are concatenations of a Padovan number and a Perrin number

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