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...

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...

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...

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...

odd 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)}...

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...

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,...

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...

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...

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...

integer sequence with characteristic equation x3 = x + 1. The Perrin numbers bear the same relationship to the Padovan sequence as the Lucas numbers do...

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

In mathematics, a Lehmer sequence is a generalization of a Lucas sequence. If a and b are complex numbers with a + b = R {\displaystyle a+b={\sqrt {R}}}...

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...

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 which...

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

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...

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

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...

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...

In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified explicitly by giving a formula...

polynomials Lagrange polynomials Lucas polynomials Spread polynomials Touchard polynomials Rook polynomials Polynomial sequences of binomial type Orthogonal...

Wieferich prime to base 68 with order 3. Let P and Q be integers. The Lucas sequence of the first kind associated with the pair (P, Q) is defined by U 0...

mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers. The test was originally developed by Édouard Lucas in 1878 and subsequently...

Loyola University Chicago Land-use change LUC, cryptosystem based on Lucas sequences Château de Luc, a French castle-ruin in the town of Luc in the Lozère...