Results 61 to 70 of about 161 (91)

Perrin numbers that are palindromic concatenations of two repdigits [PDF]

open access: yes
Let $ \{P_n\}_{n\geq 0} $ be the sequence of Perrin numbers defined by $P_0=3$, $P_1=0$,$P_2=2$ and $P_{n+3}=P_{n+1}+P_{n}$ for all $n \geq 0$. In this paper, we determine all Perrin numbers that are palindromic concatenations of two repdigits.Comment ...
Batte, Herbert, Kaggwa, Prosper
core   +1 more source

On Repdigits as Sums of Fibonacci and Tribonacci Numbers [PDF]

open access: yesSymmetry, 2020
In this paper, we use Baker’s theory for nonzero linear forms in logarithms of algebraic numbers and a Baker-Davenport reduction procedure to find all repdigits (i.e., numbers with only one distinct digit in its decimal expansion, thus they can be seen as the easiest case of palindromic numbers, which are a ”symmetrical” type of numbers) that can be ...
Pavel Trojovský
exaly   +4 more sources

Aliquot Cycles of Repdigits [PDF]

open access: yesIntegers, 2012
Abstract.Here we show that the only aliquot cycle consisting only of rep-digits in base 10 is the cycle consisting of the perfect number 6.
Florian Luca
exaly   +4 more sources

Products of three Fibonacci numbers that are repdigits [PDF]

open access: yesAdvanced Studies: Euro-Tbilisi Mathematical Journal, 2023
The authors prove that the largest instance of a product of three Fibonacci numbers being a repdigit is \(55\) (this is a product of three Fibonacci numbers, with two of such factors being \(1\)). The proof uses an approach via Baker's method to get an astronomical bound on the length (number of digits) of the repdigit in question (in this case \(3 ...
Alan, Murat, Alan, Kadriye Simsek
exaly   +5 more sources
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Associated Pell numbers which are repdigits or concatenation of two repdigits

Boletin De La Sociedad Matematica Mexicana, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zafer Siar   +2 more
exaly   +2 more sources

Repdigits in Euler functions of associated pell numbers

open access: yesProceedings of the Indian Academy of Sciences: Mathematical Sciences, 2020
Let \(\{Q_n\}\) denotes the sequence of numbers defined by \[ Q_0=1;~Q_1=1;~Q_{n+1}=2Q_n+Q_{n-1},~n\geq 1. \] Using elementary number theoretic notions, the following main result is proved: Theorem. Let \(d\in \{1,\ldots,9\}\) and \(m\in \mathbb{N}\).
G K Panda, Panda G K
exaly   +2 more sources

k-Pell Numbers as Product of Two Repdigits

Mediterranean Journal of Mathematics, 2022
The paper deals with the investigation of generalized Pell numbers of order \(k\), which are products of two repdigits. Since last two-three decades, there has been a lot of studies that involves the search of repdigits either in a particular sequence or the sums or products of sequential terms.
Salah Eddine Rihane, Rihane Salah Eddine
exaly   +3 more sources

An Explicit Bound for Aliquot Cycles of Repdigits

Integers, 2012
Abstract.We find an explicit bound, in terms ...
exaly   +4 more sources

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