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.
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 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.
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 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.
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 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.
A "lucky number" is typically a number that people consider to bring good fortune or positive energy. The concept of lucky numbers varies across cultures and individuals. For example: 1. **Cultural Significance**: In some cultures, certain numbers are viewed as lucky due to traditional beliefs or superstitions. For instance, in Chinese culture, the number 8 is considered lucky because it sounds similar to the word for "prosperity.
Lucky numbers are a sequence of natural numbers that are generated by a specific sieve process, first introduced by the mathematician Leonhard Euler. The process of generating lucky numbers is similar to that used in the Sieve of Eratosthenes for finding prime numbers, but instead of eliminating multiples of prime numbers, it eliminates numbers based on their positions.
A Löschian number refers to a specific type of number in number theory that is connected to the properties of the Löschian polynomial. The term itself may not be widely recognized, as Löschian numbers are not a standard concept in mathematics like prime numbers or Fibonacci numbers.
A **magic constant** is the sum of the numbers in any row, column, or diagonal of a magic square. A magic square is a grid arrangement of distinct integers such that the sum of the numbers in each row, column, and both main diagonals is the same.
In physics, the term "magic number" refers to specific numbers of nucleons (protons and neutrons) in atomic nuclei that result in a nucleus being more stable than others. These magic numbers correspond to closed shells of nucleons, similar to how noble gases have filled electron shells, leading to their stability.
In mathematics, a "meander" refers to a specific type of curve or path that has a winding, zigzagging shape. More formally, a meander can be described in the context of topology and combinatorial geometry, where it often pertains to the study of curves on a plane that cross themselves in a certain way. A classic example of meanders arises in the study of river paths or the trajectory of flowing water, which tend to form intricate, looping patterns as they navigate through landscapes.
The Mian–Chowla sequence is an infinite sequence of integers defined by a specific recursive relationship. The sequence is constructed in such a way that it avoids repetitions and maintains specific properties regarding sums of elements. The definition of the Mian–Chowla sequence can be outlined as follows: 1. The first element of the sequence is 1, i.e., \( a_1 = 1 \).
The Motzkin numbers are a sequence of natural numbers that arise in various combinatorial contexts. The \(n\)th Motzkin number, denoted as \(M_n\), counts the number of ways to draw non-intersecting chords connecting \(n\) points on a circle to the diameter below, without any chords crossing each other. Additionally, it can represent the number of monotonic paths along the edges of a grid.
The Ménage problem is a classic problem in combinatorics that involves counting the number of ways to arrange couples such that no couple sits next to each other. Typically, the problem is stated with a specific number of couples, and the arrangements are considered around a circular table.