Results 31 to 40 of about 50 (49)
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Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
Mathematica SlovacaAbstractLet (Fn)n≥0and (Ln)n≥0be the Fibonacci and Lucas sequences, respectively. In this paper we determine all Fibonacci numbers which are mixed concatenations of a Fibonacci and a Lucas numbers. By mixed concatenations ofaandb, we mean the both concatenationsabandbatogether, whereaandbare any two nonnegative integers.
Altassan, Alaa, ALAN, Murat
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The continuous functions for the Fibonacci and Lucas p-numbers
Chaos, Solitons & Fractals, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stakhov, Alexey, Rozin, Boris
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Incomplete Fibonacci and Lucas numbers
Rendiconti del Circolo Matematico di Palermo, 1996It is well known that the Fibonacci numbers \(F_n\) and the Lucas numbers \(L_n\) can be written as \[ \begin{aligned} F_n &= \sum^k_{i=0} {{n-1-i} \choose i}, \qquad \lfloor (n- 1)/2 \rfloor\leq k\leq n-1, \tag{1}\\ L_n &= \sum^k_{i=0} {n\over {n-i}} {{n-i} \choose i}, \qquad \lfloor n/2 \rfloor \leq k\leq n-1.
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Fibonacci and Lucas numbers which are product of two Jacobsal-Lucas numbers
2023In this study, we find all Fibonacci numbers F-k and Lucas numbers L-k which are products of two Jacobsthal-Lucas numbers. More generally, taking k, m, n as nonnegative integers, we proved that F-k = j(m)j(n) = (2(m) + ((-1)(m)) . (2(n) + ((-1)(n)) implies that (k, m, n) = (1, 1, 1); (2, 1, 1), (3, 0, 1), (5, 1, 2), (9, 0, 4) and L-k = j(m)j(n) implies
Erduvan, F, Keskin, R
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Identities for Products of Fibonacci and Lucas Numbers
The Fibonacci Quarterly, 1967Daykin, D. E., Dresel, L. A. G.
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Repdigits as sums of four Fibonacci or Lucas numbers
J. Integer Seq., 2018The Fibonacci sequence \((F_n)_{n\ge 0}\), is defined by the linear recurrence \(F_0=0\), \(F_1=1\), and \(F_{n+2}=F_{n+1}+ F_n\) for all \(n\ge 0\). The Lucas sequence \((L_n)_{n\ge 0}\), is defined by the same recurrence but with different initial terms, \(L_0=2\) and \(L_1=1\).
Benedict Vasco Normenyo +2 more
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Fibonacci numbers which are concatenation of three Fibonacci or Lucas numbers
Punjab University Journal of MathematicsIn this note, we show that there is no Fibonacci number that can be expressed as a concatenation of three Fibonacci or Lucas numbers under a certain constraint. That is, we solve to the Diophantine equations Fn = 10d+lFm1 + 10lFm2 + Fm3 and Fn = 10d+lLm1 + 10lLm2 + Lm3 in non-negative integers (n, m1, m2, m3) with m2 ≤ m1, where d and l represent the ...
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Simple integral representations for the Fibonacci and Lucas numbers
2022Summary: Integral representations of the Fibonacci numbers \(F_{kn+r}\) and the Lucas numbers \(L_{kn+r}\) are presented. Each is established using methods that rely on nothing beyond elementary integral calculus.
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