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On b-repdigit polygonal numbers [PDF]

Notes on Number Theory and Discrete Mathematics
We prove a finiteness theorem concerning repdigits in base b ≥ 2 represented by a fixed quadratic polynomial. We also show that there is a finite number of polygonal numbers that are also b-repdigits for all b ≥ 2 provided that $(b,s) \notin \left\{\left(\frac{8(s-2)}{(s-4)^{2}}d+1,s\right):s \in [3,13]-\{4\}\right\}$, where s ≥ 3 denotes the number of
Adriana Mora, Eric Bravo
exaly   +3 more sources

Curious Generalized Fibonacci Numbers

Mathematics, 2021
A generalization of the well-known Fibonacci sequence is the k−Fibonacci sequence whose first k terms are 0,…,0,1 and each term afterwards is the sum of the preceding k terms. In this paper, we find all k-Fibonacci numbers that are curious numbers (i.e.,
Jhon Jairo Bravo Grijalba, JOSÉ L Herrera, CARLOS Gomez   +2 more
exaly   +3 more sources

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Associated Pell numbers which are repdigits or concatenation of two repdigits

Boletín de la Sociedad Matemática Mexicana, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sai Gopal Rayaguru, Gopal Krishna Panda, Zafer Şiar   +2 more
openaire   +1 more source

Repdigits as products of two Fibonacci or Lucas numbers

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2020
Let \( (F_n)_{n\ge 0} \) and \( (L_n)_{n\ge 0} \) be the sequences of Fibonacci and Lucas numbers given by \( F_0=0, ~ F_1=1, ~ L_0=2, ~L_1=1 \), \( F_{n+2}=F_{n+1}+F_n \), and \( L_{n+2}=L_{n+1}+L_n \) for all \( n\ge 0 \), respectively. A repdigit is a positive integer \( N \) that has only one distinct digit when written in its decimal expansion ...
Refik Keskin
exaly   +3 more sources

Repdigit sokszögszámok, repdigit középpontos sokszögszámok

Debreceni szemle
Az előadás összefoglalója: A matematikában repdigit számoknak nevezzük azokat az egész számokat, amelyeknek minden számjegye megegyezik. A tízes számrendszerben erre példa a 222, 55555, stb. Ez általános alakban a d((10^k-1)/9) képlettel adható meg, ahol d jelöli az ismétlődő számjegyet, vagyis d az {1, 2, 3,...,9} halmaz eleme, k pedig a számjegyek ...
exaly   +2 more sources

Aliquot Cycles of Repdigits

Integers, 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, Herman te Riele
openaire   +2 more sources

Repdigit Keith numbers

Lithuanian Mathematical Journal, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jhon Jairo Bravo Grijalba, Florian Luca, Luca Florian   +2 more
exaly   +2 more sources

Lucas numbers which are concatenations of three repdigits

Results in Mathematics, 2021
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Erduvan, Fatih, Keskin, Refik, Keskin, Refik   +2 more
openaire   +3 more sources

Tribonacci numbers with two blocks of repdigits

Mathematica Slovaca, 2021
AbstractThe 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.
Jhon Jairo Bravo Grijalba, Eric Bravo
exaly   +3 more sources

Odd Repdigits to Small Bases Are Not Perfect

Integers, 2012
Abstract.We demonstrate, by considering each base in the range 2 through 9 ...
Kevin A. Broughan, Qizhi Zhou
exaly   +4 more sources