Lucas numbers

Lucas numbers

[′lü·kəs ‚nəm·bərz]
(mathematics)
The terms of the Fibonacci sequence whose first two terms are 1 and 3.
References in periodicals archive ?
These convolutions were introduced in [3] for Fibonacci and Lucas numbers and studied in many recent papers, for example, [4-9], also with their extensions to Fibonacci, Lucas, and Chebyshev polynomials.
Hoggatt, Jr.: Fibonacci and Lucas Numbers, 1969, The Fibonacci Association, Santa Clara, 1979.
The problem of finding for Fibonacci and Lucas numbers of a particular form has a very rich history.
Division of Science, Mathematics, and Engineering--USC Sumter Connections between Fibonacci Numbers and Lucas Numbers
and the Lucas numbers L = [l.sub.n] = ..., -4,3, -1,2,1,3,4, ..., which are named after the French mathematician Edouard Lucas.
By setting x = 1 in these corollaries, we can easily deduce the following interesting identity involving the Fibonacci numbers and the Lucas numbers.
And the many interrelations that continue to be found between Fibonacci numbers, Lucas numbers, the golden section, and geometrical patterns in nature are startling enough to call for periodic international conferences to discuss them.
Lahr, "Fibonacci and Lucas Numbers and the Morgan-Voyce Polynomials in Ladder Network and in Electric Line Theory," Fibonacci Numbers and Their Appl., Vol.
There are many very interesting and important results related to Fibonacci numbers and Lucas numbers; some of them can be found in Yi and Zhang [14], Ozeki [15], Prodinger [16], Melham [17], and Wang and Zhang [18].
Fibonacci and Lucas numbers of the form [2.sup.a] + [3.sup.b] + [5.sup.c] Diego MARQUES and Alain TOGBE Communicated by Shigefumi MORI, M.J.A.
For example, they proved that 2 and 3 are the only solutions of K(n) = [n.sup.2]; If a, b > 5, then K(a x b) > K(a) x K(b); If a > 5, then for all positive integer n, K([a.sup.n]) > n x K(a); The Fibonacci numbers and the Lucas numbers do not exist in the sequence {K(n)}; Let C be the continued fraction of the sequence {K(n)}, then C is convergent and 2 < C < 3; K([2.sup.n]-1)+1 is a triangular number; The series [[infinity].summation over (n=1)] 1/K(n) is convergent.
have widely applications in many fields [1-4], contact closely with Fibonacci numbers, Lucas numbers [5-6], and so on.