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  2. Look-and-say sequence - Wikipedia

    en.wikipedia.org/wiki/Look-and-say_sequence

    Look-and-say sequence. The lines show the growth of the numbers of digits in the look-and-say sequences with starting points 23 (red), 1 (blue), 13 (violet), 312 (green). These lines (when represented in a logarithmic vertical scale) tend to straight lines whose slopes coincide with Conway's constant. In mathematics, the look-and-say sequence ...

  3. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    The sequence of numbers involved is sometimes referred to as the hailstone sequence, hailstone numbers or hailstone numerals (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), [5] or as wondrous numbers. [6] Paul Erdős said about the Collatz conjecture: "Mathematics may not be ready for such ...

  4. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    Recamán's sequence: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence. A005132: Look-and ...

  5. Fermat's Last Theorem - Wikipedia

    en.wikipedia.org/wiki/Fermat's_Last_Theorem

    Fermat–Catalan conjecture. In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many ...

  6. Eight queens puzzle - Wikipedia

    en.wikipedia.org/wiki/Eight_queens_puzzle

    Eight queens puzzle. The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. The problem was first posed in the mid-19th century.

  7. Tournament (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Tournament_(graph_theory)

    Tournament (graph theory) In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions. Equivalently, a tournament is an orientation of an undirected complete graph. (However, as directed graphs, tournaments are not complete: complete directed graphs have two edges, in ...

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