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2. Busy beaver - Wikipedia

   en.wikipedia.org/wiki/Busy_beaver

   Learn about the busy beaver game, a theoretical computer science challenge to find the best Turing machine with n states. Discover the uncomputable functions related to the game, such as Σ (n) and S (n), and their implications for computability theory.

3. Order of operations - Wikipedia

   en.wikipedia.org/wiki/Order_of_operations

   Learn the rules and conventions for evaluating mathematical expressions with different operations and precedences. Find out how to use parentheses, exponents, roots, fractions, and other symbols of grouping to avoid ambiguity.

4. Lexicographic order - Wikipedia

   en.wikipedia.org/wiki/Lexicographic_order

   Lexicographic order is a generalization of the alphabetical order to sequences of symbols or elements of a totally ordered set. It is used in mathematics, combinatorics, and computer science to compare and sort words, strings, and subsets.

5. Collatz conjecture - Wikipedia

   en.wikipedia.org/wiki/Collatz_conjecture

   The Collatz conjecture is a famous unsolved problem in mathematics that asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. Learn about the history, statement, complexity, and partial results of this conjecture, also known as the 3x + 1 problem or the hailstone sequence.

6. Farey sequence - Wikipedia

   en.wikipedia.org/wiki/Farey_sequence

   A Farey sequence of order n is a list of fractions with denominators less than or equal to n, arranged in increasing order. Learn about the properties, examples, and applications of Farey sequences, also known as Farey series.

7. Pell number - Wikipedia

   en.wikipedia.org/wiki/Pell_number

   In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins ⁠ 1 / 1 ⁠ , ⁠ 3 / 2 ⁠ , ⁠ 7 / 5 ⁠ , ⁠ 17 / 12 ⁠ , and ⁠ 41 / 29 ⁠ , so the sequence of Pell ...