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.

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.

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 \(L_1 = 1\).

A Mersenne prime is a specific type of prime number that can be expressed in the form \(M_n = 2^n - 1\), where \(n\) is a positive integer. In other words, if \(M_n\) is prime, then \(n\) itself must also be prime.

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.

In number theory and combinatorics, the **partition function** is a function that counts the number of distinct ways a given positive integer can be expressed as a sum of positive integers, regardless of the order of addends.

A primorial is a product of the first \( n \) prime numbers. It is denoted as \( p_n\# \), where \( p_n \) is the \( n \)-th prime number.

The Schröder numbers are a sequence of numbers in combinatorial mathematics that count certain types of lattice paths or combinatorial structures. Specifically, they can be used to count the number of ways to connect points in a grid using non-crossing paths that adhere to specific restrictions.

The Schröder–Hipparchus number, denoted \( \text{SH}(n) \), is a sequence of numbers that counts the different ways to draw non-crossing partitions of a set with \( n \) elements. Specifically, these numbers are related to various combinatorial structures, including certain types of trees and the enumeration of non-crossing partitions.

"Sequences" is a book written by American author and poet, John R. McTavish. It comprises a collection of poems that explore various themes, including nature, humanity, and the interconnectedness of life. The work delves into the experiences and emotions that shape human existence, often employing vivid imagery and reflective language.

The number 10 is a numerical digit that represents the integer between 9 and 11. In various contexts, it can have different meanings: 1. **Mathematics**: It's a base-10 number, which is significant in the decimal system. 2. **Counting**: It’s the first two-digit number. 3. **Ratings**: In many scoring systems, a score of 10 often indicates the highest rating, denoting excellence or perfection.

A **sum-free sequence** is a sequence of integers such that no two elements in the sequence sum to another element in the same sequence. In other words, if \( a \) and \( b \) are elements of the sequence, then \( a + b \) should not be an element of the sequence.

A Woodall number is a specific type of number in number theory that is defined as a number of the form \( n \cdot 2^n - 1 \), where \( n \) is a positive integer.

The number 24 is a natural number that follows 23 and precedes 25. It is an even number and is often recognized for several mathematical and cultural significances. Mathematically, here are a few interesting facts about the number 24: 1. **Factorization**: 24 can be factored into prime numbers as \( 2^3 \times 3 \).

10,000,000 is a numerical figure that represents ten million. It's often used in finance, statistics, and various contexts to indicate a large quantity or amount. In numeric form, it can also be expressed as \( 10^7 \) in scientific notation.

The number 1001 is an integer that follows 1000 and precedes 1002. It is often recognized for its mathematical properties and cultural references. For instance: 1. **Mathematical Properties**: - It is an odd number. - It is a composite number, as it can be divided by numbers other than 1 and itself. Specifically, 1001 can be factored into prime numbers as \(7 \times 11 \times 13\).

The number 144,000 can have different meanings depending on the context: 1. **Numerical Value**: Mathematically, 144,000 is simply a large integer. 2. **Biblical Reference**: In the Book of Revelation in the Christian Bible, 144,000 is mentioned as the number of servants of God who are sealed from the tribes of Israel. This has been interpreted in various ways by different religious groups.

The number 109 is a natural number that follows 108 and precedes 110. It is an odd number and is classified as a prime number because it has no positive divisors other than 1 and itself. In the context of mathematics, it can be used in various calculations, sequences, or as a representation of a quantity.

The number 141 is a positive integer that comes after 140 and before 142. It can be expressed in various contexts: 1. **Mathematics**: - It is an odd number. - It is a composite number, as it has divisors other than 1 and itself. The prime factorization of 141 is \(3 \times 47\).

The number 177 is a natural number that comes after 176 and before 178. It is an odd number and can be classified in several contexts: 1. **Mathematics**: - 177 is the sum of three consecutive prime numbers: 59 + 61 + 57. - It can be factored into its prime components as \(3 \times 59\).