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For an integer $k \geq 2$ , let ${(n)}_{n}$ be the $k -$ generalized Pell sequence which starts with $0, ..., 0, 1$ ( $k$ terms) and each term afterwards is given by the linear recurrence $n = 2 n - 1 + n - 2 + \dots + n - k$ . In this paper, we find all $k$ -generalized Pell numbers with only one distinct digit (the so-called repdigits). Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for repdigits in the usual Pell sequence ${(P_{n}^{(2)})}_{n}$ .

Repdigits in the base $b$ as sums of four balancing numbers

Refik Keskin, Faticko Erduvan (2021)

Mathematica Bohemica

The sequence of balancing numbers $(B_{n})$ is defined by the recurrence relation $B_{n} = 6 B_{n - 1} - B_{n - 2}$ for $n \geq 2$ with initial conditions $B_{0} = 0$ and $B_{1} = 1 .$ $B_{n}$ is called the $n$ th balancing number. In this paper, we find all repdigits in the base $b,$ which are sums of four balancing numbers. As a result of our theorem,...

Řetězové zlomky [Book]

Chinčin, A. Ja. (1952)

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Regularity of distribution of (nα)-sequences

Relations de dépendance linéaire entre des logarithmes de nombres algébriques

Remark on periodic solutions of a linear wave equation in one dimension

Remarks on the arithmetic properties of the values of hypergeometric functions

Remarks on the Irrationality and Transcendence of Certain Series.

Remarks on the theory of diophantine approximation

Remarques sur les nombres de Pisot-Vijayaraghavan

Répartition de $λ α^{n}$ dans les adèles

Répartition des valeurs de la fonction «somme des chiffres»

Répartition des valeurs d'une somme de fonctions exponentielles

Répartition (mod 1) des puissances successives des nombres réels.

Répartition modulo 1 dans un corps de séries formelles sur un corps fini [Book]

Repdigits in generalized Pell sequences

Repdigits in the base $b$ as sums of four balancing numbers

Repetitiveness in binary recurrences.

Representation of real numbers as sums of $U_{2}$ -numbers

Representations of integers as sums of primes from a Beatty sequence

Representations of integers by binary forms and the rank of the Mordell-Weil group.

Results on the ratios of the terms of second order linear recurrences

Řetězové zlomky [Book]

Currently displaying 21 – 40 of 44