A Lucas–Carmichael number is a special type of composite number that generalizes the concept of Carmichael numbers. Specifically, a natural number \( n \) is referred to as a Lucas–Carmichael number if it satisfies the following conditions: 1. \( n \) is a composite number.

The Lucas sequence is a series of numbers that is similar to the Fibonacci sequence.

Lucas numbers are a sequence of numbers that are similar to the Fibonacci numbers but start with different initial values. The Lucas sequence is defined as follows: 1. The first two terms of the sequence are \(L_0 = 2\) and \(L_1 = 1\).

The term "Lucas chain" could refer to a couple of different concepts depending on the context, but it is most commonly associated with the Lucas sequence, which is a mathematical sequence closely related to the Fibonacci sequence.

A Lobb number is a term used in the context of graph theory to refer to a specific characteristic of a graph related to its properties concerning the number of edges and vertices. However, the term "Lobb number" might not be widely recognized or defined in standardized graph theory literature.

A list of integer sequences typically refers to various collections of sequences made up of integers that follow specific patterns or rules. These sequences can be found in mathematical literature and often have interesting properties or applications in number theory, combinatorics, and computer science. One prominent source for integer sequences is the **OEIS (Online Encyclopedia of Integer Sequences)**, which catalogs a vast number of integer sequences along with their definitions, formulas, theorems, and historical context.

A Leyland number is a specific type of integer that is defined in a mathematical context. Specifically, a Leyland number is of the form \( a^b + b^a \), where \( a \) and \( b \) are positive integers greater than or equal to 1. The interest in Leyland numbers is largely due to their properties in number theory and their applications in computational mathematics.

Leonardo numbers are a sequence of numbers that are defined similarly to the Fibonacci numbers, but with a different starting point and recurrence relation.

A Lehmer sequence is a specific type of sequence that is generated using the properties of numbers in a deterministic manner. It is defined by a recurrence relation with integer coefficients. The Lehmer sequence \( L(n) \) is typically constructed as follows: 1. The initial terms of the sequence are defined as: - \( L(0) = 0 \) - \( L(1) = 1 \) 2.

The Lazy Caterer's sequence is a sequence of numbers that represents the maximum number of pieces of cake (or any flat, two-dimensional object) that can be obtained by making a certain number of straight cuts. The sequence starts with zero cuts and progresses as follows: 1. For zero cuts, there is one piece (the whole cake). 2. For one cut, there are two pieces. 3. For two cuts, if the cuts intersect, there can be four pieces.

In combinatorics, a "large set" typically refers to a set whose size (or cardinality) is significantly large in comparison to some other relevant quantity or in the context of the problem being studied. The notion of "large" can be context-dependent and may relate to different concepts in various combinatorial settings, such as the size of the set in relation to its properties, the size of a family of sets, or the number of elements fulfilling certain conditions.

The Lambek–Moser theorem is a result in the field of mathematical logic and category theory, specifically concerning the structure of certain types of algebraic systems. It is often cited in the context of combinatory logic and the study of proof theories. In simple terms, the theorem provides conditions under which certain kinds of structures (like categories or algebraic theories) can represent a certain type of logic system.

The Lah number, denoted as \( L(n, k) \), is a combinatorial number that counts the number of ways to partition \( n \) labeled objects into \( k \) non-empty unlabeled subsets. It can be derived from Stirling numbers of the second kind, denoted \( S(n, k) \), which counts the ways to partition \( n \) labeled objects into \( k \) non-empty labeled subsets.

The Kolakoski sequence is an infinite sequence of integers that is defined recursively. It is notable because it is self-generating and consists only of the integers 1 and 2. The sequence begins with 1 and is constructed by reading the lengths of groups of 1s and 2s as specified by the terms of the sequence itself. The construction process goes as follows: 1. Start with the initial term: \( 1 \).

The Katydid sequence, also known as the "katydid word sequence," is a specific sequence of numbers defined by a recursive process based on the number of syllables in the word "katydid." The word "katydid" has three syllables, which influences the way the sequence is constructed. To generate the Katydid sequence: 1. Start with the first term as \( a_1 = 1 \).

A **K-regular sequence** is a specific type of sequence defined in the context of combinatorial number theory and formal language theory. More formally, a sequence is said to be K-regular if it can be recognized by a finite automaton or if it satisfies certain algebraic properties that can be expressed using K-dimensional vectors or matrices. The most common definition of K-regular sequences comes from the context of **generating functions**.

The Juggler sequence is a mathematical sequence defined for positive integers. Given a positive integer \( n \), the sequence is generated according to the following rules: - If \( n \) is even, the next term is calculated as \( \sqrt{n} \). - If \( n \) is odd, the next term is calculated as \( \sqrt{3n} \).

The Journal of Integer Sequences (JIS) is a peer-reviewed open-access journal that publishes research articles focused on the study of integer sequences. It is dedicated to the examination and exploration of sequences of integers, which are critical in various fields such as mathematics, computer science, and number theory. The journal was established in 1998, and it operates under the auspices of the University of Missouri.

Jacobsthal numbers are a sequence of integers defined by a recurrence relation.

The term "irrationality sequence" generally refers to a sequence of numbers or values that are irrational. In mathematics, an irrational number is a number that cannot be expressed as a simple fraction, meaning it cannot be written in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). Instead, the decimal representation of an irrational number is non-repeating and non-terminating.