Results 201 to 205 of about 237,797 (205)

On k-Lucas sequences

AIP Conference Proceedings, 2014
For positive integers n and k, the k-Lucas sequence is defined by the recurrence relation Ln+1 = kLn+Ln−1 with the initial values L0 = 2, L1 = k. The Lucas sequence and Pell-Lucas sequence are two special cases of the k-Lucas sequence. Using a matrix approach, we uncover some new facts concerning the k-Lucas sequence.
Jye-Ying Sia, C. K. Ho, Chin-Yoon Chong
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Palindromes in Lucas Sequences

Monatshefte f�r Mathematik, 2003
In this paper, we show that if (un)n ≥ 0 is a Lucas sequence of integers whose roots are real quadratic units (like the Fibonacci sequence, for example), then for every integer b > 1 the density of the set of positive integers n such that |un| is a base b palindrome (i.e., the string of its base b digits reads the same from the left and from the right)
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Lucas Sequences in Primality Testing

2014
Prime or composite? This classification determines whether or not integers can be used in digital security. One such way to begin testing an integers primality is with the Fermat test, which says that if n is a prime number and a is an integer then an-1 1 mod n.
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Two generalizations of Lucas sequence

Applied Mathematics and Computation, 2014
We define a generalization of Lucas sequence by the recurrence relation l m = bl m - 1 + l m - 2 (if m is even) or l m = al m - 1 + l m - 2 (if m is odd) with initial conditions l 0 = 2 and l 1 = a . We obtain some properties of the sequence { l m } m = 0 ∞ and give some relations between this sequence and the generalized Fibonacci sequence { q m } m =
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On a Class of Congruences for Lucas Sequences [PDF]

, 1996
Let ⋋,µ∈ℤ and define a sequence of integers {Hn(λ,μ)}n≥0 by the linear recurrence $$ {H_0}\left( {\lambda ,\mu } \right) = 2,{H_1}\left( {\lambda ,\mu } \right) = \lambda ,and{H_{n + 1}}\left( {\lambda ,\mu } \right) = \lambda {H_n}\left( {\lambda ,\mu } \right) + \mu {H_{n - 1}}\left( {\lambda ,\mu } \right)forn > 0. $$ (1.1)
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