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...

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

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...

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...

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)}...

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...

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...

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...

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...

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,...

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...

{\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...

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

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

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...

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...

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...

incarnation of American Zoetrope. Lucas wrote the initial script draft based on his earlier short film, but Coppola and Lucas agreed that it was unsatisfactory...

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...

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...

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

sequence is a Fermat pseudoprime to base 5 as well as a Lucas (3, −5) pseudoprime, but the converse is not true: 642,001 is both a psp-5 and a Lucas (3...

The Human Centipede 2 (Full Sequence) is a 2011 psychological body horror film written, directed, and co-produced by Tom Six. An international co-production...