Results 51 to 60 of about 161 (91)
Repdigits in k-generalized Pell sequence
, 2020 Let $k\geq 2$ and let $(P_{n}^{(k)})_{n\geq 2-k}$ be $k$-generalized Pell sequence defined by \begin{equation*}P_{n}^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+...+P_{n-k}^{(k)}\end{equation*} for $n\geq 2$ with initial conditions \begin{equation*}P_{-(k-2)}^{(k)}=P_{-(k-3)}^{(k)}=\cdot \cdot \cdot =P_{-1}^{(k)}=P_{0}^{(k)}=0,P_{1}^{(k)}=1.
Şiar, Zafer, Keskin, Refik
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Padovan numbers that are concatenations of two repdigits [PDF]
, 2020 Let $ (P_{n})_{n\ge 0} $ be the sequence of Padovan numbers defined by $ P_0=0 $, $ P_1 =1=P_2$, and $ P_{n+3}= P_{n+1} +P_n$ for all $ n\ge 0 $. In this paper, we find all Padovan numbers that are concatenations of two repdigits.
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Some Diophantine Equations involving associated Pell numbers and repdigits [PDF]
In this paper, we explore the relationship between repdigits and associated Pell numbers, specifically focusing on two main aspects: expressing repdigits as the difference of two associated Pell numbers, and identifying which associated Pell numbers can ...
Panda, Gopal Krishna +2 more
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On repdigits as product of consecutive Lucas numbers [PDF]
, 2018 Let (L-n)(n >= 0 )be the Lucas sequence. D. Marques and A. Togbe [7] showed that if F-n . . . Fn+k-1 is a repdigit with at least two digits, then (k, n) = (1, 10), where (F-n)(>= 0) is the Fibonacci sequence. In this paper, we solve the equation L-n . . .
Irmak, Nurettin, Togbe, Alain
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Repdigits as difference of two balancing or Lucas-balancing numbers [PDF]
Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we study the problem of writing repdigits as the difference of two balancing or Lucas-balancing numbers.
Panda, Gopal Krishna +2 more
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Збалансовані числа, які є конкатенацією трьох репдиджитів [PDF]
In this study, it is shown that the only balancing numbers which are concatenations of three repdigits are $204$ and $1189$. The proof depends on lower bounds for linear forms and some tools from Diophantine approximation.У цій статті ми встановили, що ...
Keskin, R., Erduvan, F.
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Narayana\u27s cows numbers which are concatenations of three repdigits in base $ρ$ [PDF]
Narayana\u27s sequence is a ternary recurrent sequence defined by the recurrence relation $\mathcal{N}_n=\mathcal{N}_{n-1}+\mathcal{N}_{n-3}$ with initial terms $\mathcal{N}_0=0$ and $\mathcal{N}_1=\mathcal{N}_2=\mathcal{N}_3=1$.
Tiebekabe, Pagdame +3 more
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Patterns obtained from digit and iterative digit sums of Palindromic, Repdigit and Repunit numbers, its variants and subsets [PDF]
, 2016 The digit and iterative digit sums of Palindromic numbers, their primes and squares, repdigit, repunit, their squares and cubes produced different patterns and sequences.
Opanuga, Abiodun A. +3 more
core
On repdigits as product of consecutive Fibonacci numbers [PDF]
, 2012 Let (F$_{n}$)$_{n\geq0}$ be the Fibonacci sequence. In 2000, F. Luca proved that F10 = 55 is the largest repdigit (i.e. a number with only one distinct digit in its decimal expansion) in the Fibonacci sequence. In this note, we show that if Fn · · · F$
Marques, Diego, Togbé, Alain
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