superset of Fermat numbers (see below). Lucas sequences are named after the French mathematician Édouard Lucas. Given two integer parameters P {\displaystyle...

The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and...

numbers pass: in this case, criteria relative to some Lucas sequence. Baillie and Wagstaff define Lucas pseudoprimes as follows: Given integers P and Q, where...

derived from it to John Pell. The Pell–Lucas numbers are also named after Édouard Lucas, who studied sequences defined by recurrences of this type; the...

related to Lucas numbers, which obey the same recurrence relation and with the Fibonacci numbers form a complementary pair of Lucas sequences. The Fibonacci...

known for his study of the Fibonacci sequence. The related Lucas sequences and Lucas numbers are named after him. Lucas was born in Amiens and educated at...

the Lucas sequence is the second row. See also Fibonacci integer sequences modulo n. A different generalization of the Fibonacci sequence is the Lucas sequences...

integer sequence named after the German mathematician Ernst Jacobsthal. Like the related Fibonacci numbers, they are a specific type of Lucas sequence U n...

mathematician R. D. Carmichael, states that, for any nondegenerate Lucas sequence of the first kind Un(P, Q) with relatively prime parameters P, Q and...

and composite number N is a Somer–Lucas d-pseudoprime (with given d ≥ 1) if there exists a nondegenerate Lucas sequence U ( P , Q ) {\displaystyle U(P,Q)}...

polynomial sequence which can be considered as a generalization of the Fibonacci numbers. The polynomials generated in a similar way from the Lucas numbers...

algorithm. Choose some integer A greater than 2 which characterizes the Lucas sequence: V 0 = 2 , V 1 = A , V j = A V j − 1 − V j − 2 {\displaystyle V_{0}=2...

algorithm is very similar to the Lucas–Lehmer test, but with a variable starting point depending on the value of k. Define a sequence ui for all i > 0 by: u i...

29341, 42799, 49141, and 52633 (sequence A001262 in the OEIS). The first ten strong Lucas pseudoprimes (with Lucas parameters (P, Q) defined by Selfridge's...

Lucas has founded and supported multiple philanthropic organizations and campaigns dedicated to education and the arts, including the George Lucas Educational...

{\displaystyle Cn/\log n} of the first n {\displaystyle n} terms of every Lucas sequence are practical numbers, where C > 0 {\displaystyle C>0} is a constant...

Perrin [fr], bear the same relationship to the Padovan sequence as the Lucas numbers do to the Fibonacci sequence. The Perrin numbers are defined by the recurrence...

Lehmer sequence U n ( R , Q ) {\displaystyle U_{n}({\sqrt {R}},Q)} or V n ( R , Q ) {\displaystyle V_{n}({\sqrt {R}},Q)} is a generalization of a Lucas sequence...

F_{6}=F_{5}+F_{4}=5+3=8} . The sequence 2, 1, 3, 4, 7, 11, ... of Lucas numbers satisfies the same recurrence as the Fibonacci sequence but with initial conditions...

mathematics, a Lucas chain is a restricted type of addition chain, named for the French mathematician Édouard Lucas. It is a sequence a0, a1, a2, a3,...

The sequence of Lucas numbers (not to be confused with the generalized Lucas sequences, of which this is part) is like the Fibonacci sequence, in that...

the p {\displaystyle p} -th Lucas number.: 42  McIntosh and Roettger establish several equivalent characterizations of Lucas–Wieferich primes. In particular...

preceding denominator to form the new numerator. This sequence of denominators is a particular Lucas sequence known as the Pell numbers. We can gain further...

divisibility sequence. More generally, any Lucas sequence of the first kind Un(P,Q) is a divisibility sequence. Moreover, it is a strong divisibility sequence when...

Lucas. THX 1138 is the first film of a planned seven-picture slate commissioned by Warner Bros. from the 1969 incarnation of American Zoetrope. Lucas...

as assistant editors, including George Lucas. The following spring, the newly engaged Marcia moved in with Lucas at his hilltop apartment on Portola Drive...

integers with m > 1 and k > 1. The Mersenne number sequence is a member of the family of Lucas sequences. It is Un(3, 2). That is, Mersenne number mn = 3mn−1...

if ( a n ) n ≥ 1 {\displaystyle (a_{n})_{n\geq 1}} is a Lucas sequence or a Lehmer sequence, then Z ( a n ) ⊆ { 1 ≤ n ≤ 30 } {\displaystyle {\mathcal...

first Édouard Lucas Memorial Lecture was given at the 13th ICFNTA. The Lecture is named in honor of Édouard Lucas, for whom the Lucas sequence is named. "The...

consolidated theories. Integer sequence Fibonacci sequence Golden mean base Fibonacci coding Lucas sequence Padovan sequence Figurate numbers Polygonal number...