Tribonacci numbers with two blocks of repdigits
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Eric F. Bravo
und
Jhon J. Bravo
Abstract
The Tribonacci sequence is a generalization of the Fibonacci sequence which starts with 0,0,1 and each term afterwards is the sum of the three preceding terms. Here, we show that the only Tribonacci numbers that are concatenations of two repdigits are 13,24,44,81. This paper continues a previous work that searched for Fibonacci numbers which are concatenations of two repdigits.
The authors are members of the research group: Matemática Discreta y Aplicaciones: ERM (MATDIS).
J. J. B. was supported in part by Project VRI ID 5385 (Universidad del Cauca)
Acknowledgement
We thank the reviewers for their detailed comments and suggestions which significantly contributed to improving the quality of the manuscript.
(Communicated by István Gaál )
References
[1] Alahmadi, A.—Altassan, A.—Luca, F.—Shoaib, H.: Fibonacci numbers which are concatenations of two repdigits, Quaest. Math. 44(2) (2021), 281–290.10.2989/16073606.2019.1686439Suche in Google Scholar
[2] Baker, A.—Davenport, H.: The equations 3x2 − 2 = y2and 8x2 − 7 = z2, Q. J. Math. 20 (1969), 129–137.10.1093/qmath/20.1.129Suche in Google Scholar
[3] Banks, W. D.—Luca, F.: Concatenations with binary recurrent sequences, J. Integer Seq. 8 (2005), Art. 05.1.3.Suche in Google Scholar
[4] Bravo, J. J.—Gómez, C. A.—Luca, F.: Powers of two as sums of twok–Fibonacci numbers, Miskolc Math. Notes 17 (2016), 85–100.10.18514/MMN.2016.1505Suche in Google Scholar
[5] Bravo, J. J.—Luca, F.: On a conjecture about repdigits in k–generalized Fibonacci sequences, Publ. Math. Debrecen 82 (2013), 623–639.10.5486/PMD.2013.5390Suche in Google Scholar
[6] Bugeaud, Y.—Mignotte, M.—Siksek, S.: Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers, Ann. of Math. (2) 163 (2006), 969–1018.10.4007/annals.2006.163.969Suche in Google Scholar
[7] Dujella, A.—Pethő, A.: A generalization of a theorem of Baker and Davenport, Q. J. Math. 49 (1998), 291–306.10.1093/qmathj/49.3.291Suche in Google Scholar
[8] Luca, F.: Fibonacci and Lucas numbers with only one distinct digit, Port. Math. 57 (2000), 243–254.Suche in Google Scholar
[9] Marques, D.: Onk–generalized Fibonacci numbers with only one distinct digit, Util. Math. 98 (2015), 23–31.Suche in Google Scholar
[10] Marques, D.—Togbé, A.: On terms of linear recurrence sequences with only one distinct block of digits, Colloq. Math. 124 (2011), 145–155.10.4064/cm124-2-1Suche in Google Scholar
[11] Matveev, E. M.: An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers II, Izv. Ross. Akad. Nauk Ser. Mat. 64 (2000), 1217–1269.10.1070/IM2000v064n06ABEH000314Suche in Google Scholar
[12] Qu, Y.—Zeng, J.: Lucas numbers which are concatenations of two repdigits, Mathematics 8 (2020), 1–8.10.3390/math8081360Suche in Google Scholar
[13] Rayaguru, S. G.—Panda, G. K.: Balancing numbers which are concatenation of two repdigits, Bol. Soc. Mat. Mex. (3) 26(3) (2020), 911–919.10.1007/s40590-020-00293-0Suche in Google Scholar
[14] Sloane, N. J. et al.: The On–Line Encyclopedia of Integer Sequences, published electronically at https://oeis.org, 2021.Suche in Google Scholar
[15] Spickerman, W. R.: Binet’s formula for the Tribonacci numbers, Fibonacci Quart. 20 (1982), 118–120.Suche in Google Scholar
© 2021 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- Prof. RNDr. Michal Fečkan, DrSc. – Sexagenarian?
- Tribonacci numbers with two blocks of repdigits
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- A nonparametric estimation of the conditional ageing intensity function in censored data: A local linear approach
- Donsker’s fuzzy invariance principle under the Lindeberg condition
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- Matrix variate pareto distributions
- Global exponential periodicity and stability of neural network models with generalized piecewise constant delay
- Optimal inequalities for contact CR-submanifolds in almost contact metric manifolds
Artikel in diesem Heft
- Regular papers
- Prof. RNDr. Michal Fečkan, DrSc. – Sexagenarian?
- Tribonacci numbers with two blocks of repdigits
- Padovan numbers that are concatenations of two distinct repdigits
- On the 2-rank and 4-rank of the class group of some real pure quartic number fields
- A general inverse matrix series relation and associated polynomials – II
- Some hardy type inequalities with finsler norms
- Starlikeness and convexity of the product of certain multivalent functions with higher-order derivatives
- Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle
- How is the period of a simple pendulum growing with increasing amplitude?
- Fourier transforms of convolution operators on orlicz spaces
- Some characterizations of property of trans-Sasakian 3-manifolds
- P-Adic metric preserving functions and their analogues
- On statistical convergence of sequences of closed sets in metric spaces
- A characterization of the uniform convergence points set of some convergent sequence of functions
- A nonparametric estimation of the conditional ageing intensity function in censored data: A local linear approach
- Donsker’s fuzzy invariance principle under the Lindeberg condition
- Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics
- Matrix variate pareto distributions
- Global exponential periodicity and stability of neural network models with generalized piecewise constant delay
- Optimal inequalities for contact CR-submanifolds in almost contact metric manifolds
